Looking at the pix of your joists, it seems that the only thing in your way other than the x bracing is a few wires and a pipe or two;
I doubt you'll be happy with your isolation if you don't take care of the upper leaf first, this will make a VERY noticeable difference. Here's what I'd do -
Temporarily remove ALL those cross-braces; it's not gonna make anything fall down short term, those are just to keep your floor from learning how to squeak and your joists from twisting since they're only held captive at the two ends.
Precut all the inserts you're going to use in one joist bay, and if your joists aren't quite parallel make sure each insert is numbered or otherwise marked so you know where it will fit; these don't have to be a really tight fit, because you're gonna use mud to make up the difference.
Fill all those cracks thorougly with drywall mud, smooth the surface with the drywall knife, and while the stuff is still wet put your first insert in place (probably a 4' long piece, since it's easier to work with) - using 4 pieces of 1x scrap wood and 4 clamps (or screws), push the 4 boards END-wise up against your insert about a foot from each end, clamp or screw the 1x scraps temporarily, fill around the edges of the insert with mud, then drop the wood scraps on one side of the insert at a time and start the second layer up into the joist cavity. This will be a LOT easier if you have a helper, or two extra hands growing out of your head
Work both layers of beef-up material up into the joist cavity, filling in any void areas with drywall mud, and while it's still wet press your PERMANENT cleats up against the edges of the drywall and fasten with screws to the joist - 1 screw every 8" is plenty.
Do each joist bay the same way.
Once all the bays are done, caulk anywhere there looks like any kind of a gap, no matter how small - then replace your x braces; it's probable that you'll need to trim the braces enough to make up for the extra thickness of joists at the upper ends of each x brace due to the 1x cleating that's holding your extra layers up between joists.
In your case,
where your spans are close to max, I'd just use ONE layer of 5/8 wallboard up between joists, so you can keep your double layer UNDER along with insulation - but it's REALLY important that you mud those cracks between subfloor boards first.
Once your beef is up and the x bracing back in place, you can insulate and hang your lower layers - remember, no hard contact between any of your inner leaf and your outer leaf except between wall frames and floor - you want your inner leaf NOT flanking sound into the framework of the house... Steve
Soooo, when a Musician dies, do they hear the white noise at the end of the tunnel??!? Hmmmm...
I'm keeping my fingers crossed though that there is a solution and you can continue with the beefing up (as painful as it may be right now) since I beleive you will be happy with the extra isolation to the upstairs when all is said and done.