Due to the convoluted nature of the relevant regs, and the nebulous nature of sim authorization, I would try to obtain copies of the authorization letters for the sims you used.

If you log time in an airplane with an N-number and a type code, it is safe to assume that airplane is legal for aeronautical experience in the obvious category and class.

But they don't have that safe assumption with some random sim time, so they might ask for the LOA. I don't think they would be required to, Joe Bob's 3-Day ATP Mill probably wouldn't care. But for example an airline might be concerned about training a pilot, putting them online in revenue service and then later learning that the sim time on which their ATP eligibility was based is no bueno. Awkward and disruptive.

You'd think these schools would know this by now, and just give everyone a packet with copies of all the sim LOA's.

I would reach out to the recruiters and ask them specifically how their training department and APD's deal with this. They might take it at face value if your sim time came from a school like ERAU.

But regardless of whether anyone asks you to prove it, if you put that time on an 8700 when you apply for a rating then YOU are certifying that it's legit. Did you try contacting Riddle?