Just a quick query where are noggings, (cross members) for the studs and the angle bracing?

They are a requirement down under... not being picky just my Building Surveyor degree kicking in!!

Funny the different building codes in different countries!!!

Down here we would require two rows by guessing the height is over 9 feet.

By the way will be a great room

Hey Blonde tall Put a photo of the door frames minus the skirting /baseboards, I work constrution and may have a way to drywall the gaps .

Door Frame If the gap is the size shown in the photo all around, it is relatively small. You can buy foam backer rods that you push into the gap They sell it at home depot

http://www.homedepot.com/p/Sika-3-4-in-Closed-Cell-Backer-Rod-108130/202523820

Then apply a paintable sealant, Down here we a product called no more gaps, I'm sure there would be ample products in the USA. I use acrylic sealants as they are easy to smooth over, use a damp sponge to smooth then simply paint over with the same wall paint.

Now for your baseboard. To be honest I don't know the look you are going for but to patch along the entire floor will be a bit of a nightmare. Another option would be flat aluminium skirting that you simply glue on. They are about 1.6mm thick and would be high enough to cover the drywall gaps.

http://criterionindustries.com.au/decorum-flat/

or http://www.archskirt.com.au/skirtingsuites.htm

I know these are in Australia but I'm sure you will be able to source them locally. It is simply flat bar aluminium, anodized aluminium would go with a the sci fi theme

Hope this helps or gives some ideas

Your welcome, I can offer virtually zero in advice in regards to repairing pinball machines but when it comes to construction I know a thing or two

Stupid question in the USA dont you have separate storm water and sewerage systems?