Check your booking app's time zone settings first. Mine was set to a different zone and it kept merging appointments that overlapped by a few minutes, which sounds close to what you're dealing with. Also call the software company and make them walk you through your slot rules, because most of them let two people grab the same chair if the buffer is set to zero. Set a hard 10 minute pad on every single slot, not just every third one, and turn off instant booking so your front desk can eyeball it before it locks in.

The part about them calling it a "standard onboarding charge" is what gets me, because that phrase is doing a lot of work. It sounds so boring and normal that most people just pay it and move on, which is exactly why they try it. What you did with the signed scope doc is the whole ballgame though, because now the burden flips and they have to either point to where that fee was agreed to or admit there is no such line. I bet if you had called instead of emailed, you would have gotten a totally different runaround, since a paper trail scares them way more than a phone call ever will. Feels like this kind of padding is less about the money and more about testing who is actually reading the invoice line by line.