We were just at Doune and Stirling castles last week (Tuesday) and although Doune was pretty relaxed as they had only re-opened the day before, Stirling was much busier. I couldn't tell if people were getting in without slots, but it was pretty busy for our 12n slot.
I was the planner of our four person trip and if one of our party hadn't felt strongly about Stirling, I would have skipped it.
I can say that Edinburgh Castle was a mess last Friday, although I understand the early mess is trivial compared to later in the day. We had pre-booked 9:30am slots (opening) and they were stating to the large group of slot-less people that 2pm was the first available opening and they'd better rush to the kiosks. We had joined Historic Environment Scotland for the trip and the tickets were free, so gambling on a specific time was zero added cost. As an aside, on our three week trip we saved over 1/2 on admissions with the membership, and Stirling and Edinburgh alone are almost breakeven.
If your selected operator has actually failed to reply, I'd look elsewhere. Expecting international visitors (assuming you are one) to "call", possibly facing voice messages, hold times, and "could you please hold" and the associated call costs rather than explaining the issues up front in a FAQ or replying to email is a blinking red light in my book, and I'd run the other way.
