The partial trust requirement of your hoster is odd, since Microsoft has provided guidance to hosters that they should migrate away from Medium Trust and use proper OS-level isolation instead (see here and here and here). The official position of the ASP.NET team is that Medium Trust is obsolete, which means that new features and frameworks wont be tested for partial trust support and bugs in that area won't get fixed.
Nevertheless, there are other frameworks that will run in partial trust:
- Simple Injector (which I maintain) is designed and tested for partial trust scenarios.
- Ninject has special builds for medium trust environments.
There might be others, but these are the ones I know of.