Basement studio: joists between joists?

Hiya, I'm at the end of my demolition process. Attached are several pics to show you what I've got. If you need more detailed pics to comment, I'll be glad to oblige. What you're seeing is a picture of a frame which was there, made of 2x2s and 2x4s, constructed sometime in the 1970s and covered with half-inch USG drywall (woodgrained!). During the life of the basement, there sprung a leak, which has since been repaired*, but did cause damage to the wood framing (I included a detail of a typical joint). The drywall I carefully cut down in 14-1/2 inch strips to use as a first layer against the subflooring. I've also let the furring strips remain because they're great references, a perfect 12-inch OC installation. I'll take them down in due time. I was going to let the frame remain. My room dimensions will probably (haven't finalized, yet) allow for clearance between the old frame and new frame. Any thoughts? Thanks, Dave *Note--we had this recent storm, "The October Surprise." Most of the houses on my street had flooded basements. I had nary a drop of water.

Okay, I've used the calculators and I'm fairly confident, but there's always that tick of doubt because I'm not a pro (got the Gervais book, btw. Well worth the $25). For ceiling/floor engineering purposes, here's what I have: Two 10' spans are supported by a 6"x8" beam, which is in turn supported by poles at 10' intervals. The joists are 12' lengths of 2"x8" nominal indeterminate pine or fir (whatever was common in Tonawanda in 1925) at 16" oc. The floor above is 3/4" t&g with 3/4 strip hardwood flooring. The calculator says I have plenty of pounds/per to spare, such that I can hang just about as many layers of gypsum boards as I want. Any corrections or warnings? Dave