There are many ways to support this section of your shower. You would need access from below. Can you gain access and then post a couple of pictures?
With a few simple Strong Tie Brackets and some common 2"x4" stock you would be able to support the area around the drain.
We love working with spray foam products and you might weight the drain area with a garbage can of water 15 Gallons or so should give you a 120 pound brace and then spray foam the area. This would work only for smaller gaps so before jumping in get the hole opened up and send us some pictures.
Do you know how to post pictures here on Terry's page?