Like I said in my first post, I can see that you are traumatised by what you went through. I'm not knocking that and I don't think you're a wuss.
If you discuss with your GP about the monitoring they can provide, you would still be in control because you'd be driving that process.
Fwiw, if you were my friend or family member I'd have asked you the same questions - my concern is you're about to shell out significant sums of money on private tests that won't come with the level of explanation, oversight and aftercare that you need and deserve.
Which won't bring you the reassurance or control you're seeking.
As pp says, you have a legitimate basis to approach your GP for follow-up monitoring. It would seem worth exhausting that option before spending lots of money on private tests.
Depending on how phlebotomy services are delivered where you live, it could be as quick as the GP printing the blood test form in your appointment and you going to a blood test appointment the next day with results within days.
Also, the blood test form might only seem to be a short list but eg FBC and LFT come back as a whole list of different results. A single entry on the blood request form doesn't equate to a single test, but the NHS doesn't always explain that because they're not trying to sell themselves to you.
Those private websites are listing everything separately for marketing reasons (listing all the different tests within liver function tests sounds more impressive and "value for money" than just saying liver function tests/ LFT), it's not necessarily any more comprehensive than what your GP could order for you.