The sony crt would likely have to use a VGA to component transcoder to keep from going digital analog digital from the original board. I am not sure how mame would output to the set. I assume you are saying I would have to output mame as 480p fixed as it would upscale anything lower than 480p? Is the output of that upscale worse than a LCD?
I haven't experienced MAME through a RGB(VGA)>Component transcoder myself, I suppose a pure transcoder wouldn't mind any resolution at whatever refresh rate, but yes the issue here would indeed be the Sony's forced conversion of anything below 480p to 480i. My experience of that sort of forced interlacing at least is that it looks ugly on a CRT no matter what.
So if you have something like a MAME set up to output real arcade low resolutions it won't look good, and if you set it up to output a fixed 480p instead with everything scaled to that you will have a choice of unfiltered, which might show ugly scaling artifacts/shimmering, or filtered which will defeat the true low res look (you can sharpen the bilinear using prescale 2 but I can only speculate about the resulting looks)
Over a flat panel MAME does fine with the same scaling options and it offers more filters beyond bilinear but that Voodoo card might not be able to pull out CRT shaders and similar refinements (fake scanlines whether from within MAME or using an SLG3000 as I've mentioned are other options) but it won't look anything like a real low res CRT either.
The freesync I would have to use a VGA -> HDMI converter for the original hardware, but gain freesync for mame. I am not seeing any 32" freesync monitors with a vga input though?
Nope forget about FreeSync with that PC no matter what, FreeSync requires both a compatible branded card and monitor, and in most cases it works only either straight via DisplayPort or HDMI on a select number of displays.
If you're worried about support for all kinds of refreshes and resolutions, try the Viewsonic VX3276-mhd, it's a monitor known to be quite liberal despite not being FreeSync nor G-Sync compatible. It's a quality IPS monitor but like most IPS displays it can come with a degree of backlight bleed (brighter 'stains' of light visible on dark backgrounds caused by loose backlight-against-lcd-panel sealing) so choose your seller well and check their returns policy in case you're not satisfied.
Normally it should also take CRT_Emudriver and display most refreshes without trouble, but again I doubt you'll get any sort of variable refresh with MAME using that Midway custom PC since CRT_Emudriver requires a compatible AMD card in any case.
Or maybe there's a way straight from MAME using the default old built-in switchres option, but that would also require to use GroovyMAME for certain reasons and I'm not sure if you can do it like that, I'd recommend you talk with Calamity.
I'm gonna ask a stupid question I should have asked way sooner to clear a potential misunderstanding on my part; do you really plan on using the PC inside that cabinet to run MAME and play all kinds of games?
New LCD TVs have done away with VGA and component inputs also.
Depends where you are, I live in Europe and there's still a number of new entry-level Full-HD TVs you can buy (mainly online) and featuring VGA/Component.
Might not be the same on the American market though, yes, or maybe it's only digital signage products.
The other issue I have is the physical constraints of the cabinet though large the maximum theoretical widescreen I can fit is 37". They don't seem to make anything in between 32" and 37" for a flat panel. I found a 37" used, they seem to have stopped manufacturing these as well, but I am not 100% sure I can make it fit by removing the bezel without buying it and then I can't return it. The maximum size of CRT is likely 36" for a television, but 32-34 would be much easier to deal with based on weight.
Indeed these days it jumpt to 43", nothing in-between.