A couple of points, yes, relays can be very reliable, the telephone exchanges I worked on years ago basically worked on relay switching, so lots of relays, operating almost continuously and it was rare for a relay to fail - but these were bigger relays than the tiny ones used in PIDs.
I would not trust the rating of the PID relay, it's likely to be over-rated and be operating very close to its limit at the amps you're talking about. If you can find a higher rated relay and replace the one inside it would, I think, be a prudent move.
My PID had a relay output, but I replaced the relay with wire links and use an SSR as I feel it is the better option in this case.
I also keep a spare PID/SSR/temp probe, just in case of any failure (better than having to wait for the slow boat from China!!).
Having said all that, I think you should try it and then you can report to us all if it works ok ('cos I don't think anyone else has tried it yet
).