I am looking for a quite specific set of specs in a laptop and the usual suspects can't meet my requirements.
Is it on topic to ask for sites/manufacturers that do full custom builds?
Asking for where to buy is off-topic. Asking for what to buy is on-topic.
Questions that are on-topic for this site ask for a recommendation of a piece of hardware, based on a specific set of requirements. Your first paragraph here sounds a lot like that - quite a specific set of specs in a laptop.
Instead of asking where to buy, why not outsource all the work? Detail all your requirements in a question, and ask for recommendations of a laptop meeting those specifications. If none of the recommendations work out for you, then you should still have been given a supplier's name along with the recommendation, which you can use to look around for other products.