But it isn't impossible, as you've said (you even implied that a user was able to replicate it, but took a bit of time to do so). Plus, just because one user has difficulty replicating the abilities doesn't that
all (or most) users would have difficulty doing so, so it might still be possible for PA to replicate TSC's abilities. If TSC's abilities are more like items/objects with special properties rather than the abilities of the being itself, then I can accept that PA might not be able to replicate it. Also, if TSC truly can resist
Power Mimicry, you'll need to add that to TSC's profile.
Also, whether or not it's in character for PA to use time stop of TGoALID doesn't really matter much as PA has Telepathy (with Precognition added in). He can hear the thoughts of TSC (and from what I've looked up about PA, it sounds like its probably passive), so he would be able to use that to accurately predict what TSC does next (which is where Precognition comes in). Plus, PA isn't stupid, he's probably smarter than even Ainz himself (as his intellect rivals Demiurge's, who often thinks ahead of Ainz without noticing). So he'll likely turn into Ainz to gain resistance to some of TSC's hax the instance he suspects it, and can work around TSC's Psychokinesis and Molecular Manipulation from there (the offensive capabilities of which seems to be limited to speeding up molecules of the target and stopping them).
Heck, PA doesn't even need TGoALID to defeat TSC (who doesn't even seem to have resistance to Death Manipulation) as he has other methods to defeat him with through Ainz's hax (which can involve Time Stop so that PA can combo his hax on TSC).
No matter how I think about it, this would most likely end up in the same result as the Ainz vs TSC match. Only this time, TSC's opponent now has more options to defeat TSC with.