The progress on the 500E has been slow, but I'm not terribly worried; there's been no ugly discoveries at the moment, and it seems like my fears about transmission issues are unfounded. Most of the issues with regards to slow shifting and noises in reverse have nothing to do with the transmission itself but rather heavily worn rubber components that help to support the transmission and driveshaft.
Knowing that the transmission itself is likely fine is a major win. In addition to the shifter bushings, the transmission mount itself is very tired; both "guibos" on the driveshaft are heavily cracked and overdue for replacement; the noise heard in reverse was actually an insulation pad that was dropping down and rubbing on the driveshaft; ball joints, steering linkage, and the lower control arm bushings, all shot; and the shop also discovered a long-festering fuel leak coming from the charcoal canister in the driver's side wheel well.
Right now, the exhaust and the driveshaft are dropped in preparation for repairing all that I just mentioned. Once we're through that, we'll see how much the drive quality has improved and what may need to be done next.