I don't agree with joecaption, and suggest that trying a can or two of foam for less than $20, could make for a definite improvement.
I'd be tempted to try some "strong" spray foam (there are different categories, depending on what's needed), working from the crawl space. Drill enough access and air-egress holes, and work from the middle out, in all directions. The trick will be in installing the correct amount of foam, such that you don't blow the shower floor (pan) out. Plug each hole after removing the injection tube, and remember to let the stuff fully cure before testing the shower pan.
But be careful. I've seen commercial steel door thresholds blown out by too much foam being injected underneath them, requiring complete door frame replacement.