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Yep, you can purchase a PID with SSR connections already in place. Take a look at http://www.auberins.com/index.php?main_page=product_info&cPath=1&products_id=3
Did you ever get this resolved? Are you sure the heater is actually on/hot when the SSR is not enabled? SSR's, by their standard operation, will leak voltage across the AC terminals but not much current. I had the same issue you did, I was seeing almost the exact same voltages you were reading and a dim lit light. The leak through current is likely enough to power a small light as it probably only requires milliamps to illuminate. I had a scrap desktop fan I wired in to simulate a load on the SSR and the voltage leak went away, there also wasn't enough current to turn the fan. So in short, as soon as there is a load on the SSR, you should get the correct readings.