Rather than using the execution stack provided by the environment (by using the built-in calling conventions directly), you could manage your stack on the heap

Rather than using the execution stack provided by the environment (by using the built-in calling conventions directly), you could manage your stack on the heap using the linear memory facilities. Function calls are a bit more expensive, since now you need a macro to convert calling conventions. But it's definitely not impossible, and it's not even really all that hard (just tedious).