I'm not entirely sure that the browser runtimes are suited for this since I watched a friend demo-ing V86 and the amount of crashes with modern OSs just seemed to make it a toy (though I might be proven wrong).
One plausible guess I have is that they might be running out of memory since the browser runtimes are expecting the WASM code to be long lived whilst a emulator JIT by nature should be able to adapt to rapidly changing code and blows out of memory before things are cleaned up.
Presumably the crashes are happening because the instruction set implemented by the JIT is on Pentium II level and so encountering modern X86 instructions makes it fail. I am not familiar with the linked project but there is no real reason why you could not emulate a 32bit Intel perfectly in WASM. For 64bit I'm not sure if wasm64 wouldn't be required.
I think there are browser-level crashes too because you're using the WASM JIT-compiler in ways it hasn't been thoroughly tested for.
The Chromium team is pretty receptive to patches though, so for a big project like this it doesn't seem unreasonable to just patch the browser to perform well enough for your use case, and then upstream the patch so everyone has it within a few months when you're ready to launch your product.
One plausible guess I have is that they might be running out of memory since the browser runtimes are expecting the WASM code to be long lived whilst a emulator JIT by nature should be able to adapt to rapidly changing code and blows out of memory before things are cleaned up.