You're obviously paying them to keep up your tank for a reason - most likely because you just don't want to deal with it! BUT... if it was me, I'd tell the maintenance people that while you don't discount their amazing ability to detect chemical imbalances with just their eyes, (you might want to reword that!) you'd like them to test the tank for what they're dosing, and show you the results. I'd also make it clear they're going to lose a customer unless they don't test for you. If they're as confident in their skills as they say, then they should have no problem doing this for you. It'll only take a few minutes of their time, and they should have the test kits onhand anyway.
My guess is they won't do it.
Also... just noticed something else in your writeup. You say that they add 4 caps of Tech A/B every week. I'm assuming since it's a fish maintenance outfit, they're adding those 4 caps all at once, each week - into a 65g tank? From my experience, two part additives for Ca
are meant to be dosed daily, in small amounts. That way they don't cause major salinity/pH swings. Not sure how many ml a "capful" is, but I think the normal maximum dosage on all those additives is 1 ml per gallon, per day. If you add more than that, you risk making a pH spike. Could this be part of it?
Still don't think it's the temperatures, but glad to hear you at least got that under control.