I hate to recommend this because they are ancient at this point, but EMC made some short depth disk shelfs long ago that have flooded ebay:
Keep in mind the SAS expanders sort of rely (if you want to run both) on the interposer to work with SATA drives. This is from memory so it could be wrong but I think there are two different interposers you can end up with, one will let both expanders/controllers see the SATA drives and the other type of interposer only lets one of the expanders/controllers see the SATA drives because it’s missing a multiplexer.
If you had 1 more inch to work with, Inwin makes some fairly short-ish disk shelves that are modern.