What if you water the compost pile with distilled vinegar? It is stronger than what you think it is and doesn't add a bunch of chlorine or sulfur. It would have to lower the pH of the pile but It would be a crap shoot on the final pH level of the compost.
I have one of those cheap analog pH meters I use to estimate my garden soil pH without having to break out the chemical test. It took me a long time to realize with those meters YOU don't water the soil with anything and then test the pH level, you let it rain on the soil and then check the pH. That seems to be a lot more accurate on those meters reading.
You may have to let the compost break down into soil before being able to use the meter though. I've never used it on a compost pile.