Sounds very hard. For example, Rule 21.3 in MISRA C 2012 basically prohibits dynamic memory allocation (e.g. malloc, calloc, realloc, free). Implementing a browser with such restrictions would be quite misrable.

I would think the MISRA rules against dynamic memory allocation would present serious difficulty if not fundamental incompatibility when trying to implement web standards.

It is against the rules to call malloc, yes.

However, it is not against the rules to launch another process with a static amount of declared memory, then access it over shmat().

This is cheating, but could it be safer?

No.