Hi Kristie,
I am due to travel back from the States to Scotland, via Heathrow, at the end of July. My understanding is that with Scotland as your final destination, and regardless of your first UK port of entry, you need to book day 2/8 tests with CTM, and have proof of your test booking before you land in the UK. If you decide to spend 10 or more days in England, then English (rather than Scottish) rules apply, which are slightly more flexible when it comes to decide which test provider to use, although all options I could see are as expensive as CTM if not more. Unfortunately, if your final destination is Scotland and have no intention of spending 10 days in England, then there is no early way out of the quarantine ("Test to Release is not available to those travelling to Scotland").
Let's hope the USA becomes a green country!
Matteo