That's a great question that is entirely fabric-dependent.
If your formalwear is wool (for example, a tuxedo or blazer) you'd probably want to swap it out for a version of the garment which is made from Superwash wool, which is machine-washable. (Or your choice of alternative fabric.) Creating superwash wool is still a pretty chemically-intensive process, but that might not be forever: https://www.moderndailyknitting.com/community/superwash-part... It should at least cut down on your TCE exposure.
Silk is trickier -- if you wet it, you have to take great care to dry it without overheating it, while at the same time getting it to dry evenly, so you don't get watermarks on the fabric. It's doable, but it's a total PITA. The best strategy here, for me, has been to wash my silk blouses very rarely, and with a great deal of care, and tumble-dry low. I also use the 'vodka trick' I picked up working in the backroom of a theatrical costume company, many years ago -- get a bottle of cheap vodka, pour it into spritz bottle (one with a fine-mist setting -- the kind at beauty stores work great) and turn the garment inside-out; hit the pits, etc. It's safe for silk, fur, and other delicate fabrics.
If you're going to be wearing silk, do it in winter or in air conditioning :)
Fur -- well, you wouldn't have been dry-cleaning fur anyway, right? right?? This is a whole chapter on its own. (The vodka trick works tho)
Finally, there are also lots of wonderful new machine-washable fibres on the market -- tencel, etc. -- that may be suitable for formalwear.
But putting formalwear aside, the biggest problem I see is down-filled jackets and duvets. I have literally no good ideas here, other than 'wash very rarely and tumble dry low, low low'