I have one. yes it supports cocktail mode Qubes via a modified rom and the other qberts via a soft dipswitch setting

You need to flip the yoke wires to correct the image, this video by Buffett explains how https://www.youtube.com/watch?v=WP3ll7nlEEE

as for the button not working, check the wires under the control panel, make sure they are both connected, if they are try swapping it with one of the player 2 start buttons and see if that works, if it does you may only need a new button, the fire button going bad seems common on the reunion cabinets

It sounds like Maximus is losing focus, when you start it up try clicking with the left mouse button. If you get control back I would say that's the issue.
One possible work around could be to set maximus to auto boot a game on startup, then if the controls work from there then it should keep working when you exit back to maximus.
Another option is finding out if something else is starting up after maximus loads, this will be the program that is stealing focus from it, when you find out what it is, then you can set it to load before maximus starts or disable it entirely if it's unnecessary.
I'm sorry if I got too technical, I guess by now I've gotten so accustomed to all the ins and outs of emulator setups and just spout technological babble  I can keep it toned down from here on in 
It did take a long time to set up this cabinet, lots of tweaks and mods to get it running right.... I really should do a youtube video on it. should be possible now that I have a new camera again. 

No worries, happy to help.
Here is my setup, maybe it will help you get yours sorted.

For the Emulation cab I have a former Technos Wrestlefest 4 player cabinet equipped with a U5000 monitor, the computer is a HP desktop core I5 with 8GB ram, the computer is a few years old (my sister was going to bin it) and the ATI 4350, it's piped through the jpac running hyperspin and x64 mame 151 nonag version, I don't typically use Mameui with a front end because I always had conflict issues.
(I did wish to point out that I do have my old copy of maximus and it works ok as well)

I have the complete romset, got it from that well known  ;) private rom tracker a while ago, I also am running daphne and singe with complete romsets for laserdisc games. I have a pair of PCBs salvaged from old Pelican  Xbox (original) Arcade sticks set up for players 3 and 4 and those are using a mayflash driver I believe.

I have win7 x64 setup in classic desktop mode with all of the fancy aero stuff turned off
I have it set to "duplicate these displays" in display/screen resolution properties

I think maybe we did read the same pages, the missing taskbar is apparently a very rare occurrence affecting about 1% of users so you are one of the unfortunate few It seems.
I'm reading up on it and your motherboard, perhaps I'll find something and then hopefully you won't have to reinstall the whole thing.

Edit: have you tried system file checker? if not you do it by rebooting into safe mode opening run dialog and typing sfc/scannow and let it do it's thing, then reboot. (you may need a regular monitor for this step) I have read it can be a solution to this problem.

It's great that you got a working picture now, just need to work those bugs out.

Maybe adjusting the pots on the neck board will help the screen weirdness, it's my best guess since I haven't seen this often.
Definitely check if it happens when you launch your emulator front end.

I looked into the taskbar disappearing on win7, it seems that it's not very common, the suggested fixes are in this order : Windows key+D if that doesn't work then Ctrl+Alt+Delete then typing explorer.exe in the box and hitting enter, these are supposed to work but are fiddly temporary fixes.

Another fix I looked into is checking to make sure only one display is enabled in control panel, apparently sometimes a phantom display gets turned on and your taskbar is on that absent display.

Sounds like HV shutdown. Try flipping the switch back, and resetting the controls to where they were and see if it comes up.

I wonder if this monitor is fitted with some kind of inverter PCB

Glad that the adjustments cured your issue with the squishing, it's not that surprising that they have slightly differing adjustments because many arcade PCBs have sync signals that are different from one another. If you ran for example, a Mortal Kombat PCB, then it would need to be adjusted again from where it is now.
Newer monitors compensate for this automatically where as the K7000 does not, and has to be done manually.

I use 640x480 and it works on my setup. I booted up my Mame cab today to check for you and it's cutoff a little bit like yours is, but I can still figure out what to do, I imagine that is normal.
You say it's not fitting top and bottom, Did you adjust the V.Height (on some monitors it's called V.size) adjustment? I'm assuming so but if not do check that.
You can try 800x600 and see if that works better for you, I'm also fairly certain that you can set it to 1024x768 and that will work also, but I haven't tried this one myself.

Once you get your front end set up, you won't likely notice it too much, I don't.

try to adjust it out, if you can't get it looking good then it may be time for a cap kit, as one of the symptoms of needing to be recapped is crushed image on the bottom (left side if mounted vertical)
Glad you got it working, it should look better when you are running a front end or a game. Windows always looks odd in this low res state.

For the wiggling picture you should try reflowing solder on the big white resistors.
I had the shifting issue on my donkey kong until I reflowed.

I'll do what I can to get you sorted and playing games 

The strange thing here is that the sync light is going out completely, it should stay a constant split screen if soft 15khz isn't installed.
We'll see how it behaves when you install the older driver and soft15 again.

Yeah, don't use the latest one I had problems when I attempted to update, I use catalyst 11.2 If I remember correctly.
Make sure you install soft15 with admin privileges if you are running vista or win 7

once you are sure it installed correctly, look at your Jpac, is the "Sync OK" light lit when Windows boots?

Yeah I chased that issue for weeks trying to figure out why it wasn't working, finally I tried the adapter and suddenly it worked.

I heard it's because the system treats each output separately and only installs the 15khz driver on the one port but not the second, and supposedly this also happened on the ArcadeVGA cards in the past. I wanted to put it out there because I didn't want it to trip you or anybody that reads this up.

Let us know how it works for you.

Thanks for the comments on the avatar, I am a big Doctor Who fan and the Fourth is my favorite doctor too

I think you are correct with the video amps interfering with each other, there is definitely a conflict on that circuit.

I suggested the HD4350 partially because it's what I've been using in my setup for the last 5 years without issue and because they are like 14.99 on ebay last time I looked, so they won't kill your wallet.
One more tip, if and when you do get a 4350, be sure to use the main DVI port with a VGA cable adapter to pipe video into the Jpac, It never worked for me trying to run the cable from the 4350's built in VGA port.

Good luck with your project! 

I'm thinking the 8100 is the problem in your set up since you say that the picture looks good on the SFII PCB.
I haven't had good luck using those Chinese converters for much of anything.

I have a PC based cabinet myself and it too is based on the JPac, but I don't use any converter in my setup, I installed a free software solution called soft15khz, which will tell your video card directly to run at arcade resolution.
Many video cards are compatible, but if you have one that isn't then I would suggest the ATI 4350, an older card that is now pretty cheap.

I think it's a great game, if you have someone to play co-op with, I always enjoyed playing it in the arcades and on Mega Drive.
I am pretty sure that Golden Axe was only sold as a kit.