Depending on how niche the third party company is, and how large your company is, is it feasible to consider a takeover? You can then get your issues solved without having to prioritize features you don't need, you get to keep the technical staff and don't have to train up a new team in something your business may not have the expertise in.

You also get to keep the same UI, the same business logic and it means less disruption to migrate to new software.

Just a stab in the dark, probably not feasible but you are looking for interesting suggestions...