When I asked about this in that readthrough thread, a RECORD/REPLAY facility was mentioned as being part of Inform 6 (I guess the library? I don’t know much about Inform) rather than interpreters.
Poking some random recent I6 (non-PunyInform) works: both Monkeys and Car Keys (Z-code) and Oremus (which appears to be Glulx underneath the Vorple) support a REPLAY verb, which causes the interpreter to prompt for a file to load (but not a RECORD verb). And I guess it’s available in PunyInform too, since All That Shimmers… is the same.