Some advice please: I really want to be an UP completist - should I trade my BTs?

I think you just have to decide what you want more and go for it. I'm sending good vibes for you completing your Up collection! I know how hard it is. I'm an Up collector too but gave up on being a completist a long time ago because of the cost. Good luck!

I think it depends on what BTs you have. If anything recent (within the past year or so) then those you'd have to trade multiples for...

Up is going to be pretty hard to complete. There are many HIGH value pins and some that are literally impossible to get, those pesky Japanese pins and cast pins that pop up from out of nowhere. Do you really think you can obtain all of them whether or not you let your BT collection go? What happens when you get rid of all your BT's and you still need a bunch of Up pins still? Lets say you never complete but you need 3 or 4 pins after the BT collection is all gone. Are you happy at that moment? Unless you have $$$$'s ready and waiting to buy pins I don't think it's possible to be a Tangled or Up completist anymore. Real talk. You can still do Brave, Wall-E, Enchanted, a few others with some good trading, lucky breaks and buying a few but those two (Up Tangled), Marquee's, LE100's for Tink, Stitch, Jessica, etc are all but impossible anymore. Others like NBC, Alice, Ariel, Tinker Bell, Stitch, Jessica, Snow White, Sleeping Beauty, Cinderella there are just so many freakin pins, if you haven't been at it for 10+ years I don't see how you'd be a completist, so you have to constrain it to a specific genre, say "Belle in Blue" and live with that.
I know a few finally completed marquee's in the last 2 years. Because of the few marquees have skyrocketed. So if you started marquee's in the last 2 years I think it's near impossible to complete. PTD's will soon be close to the same with 160+ pins and many old ones RARELY come up anymore. If you're just starting, it's gonna be a major long road ahead. But there is always the crazy releases like the Designer sets, Enchanted/UP/Tangled BT's, PODM type pins that skyrocket in value instantly and you can trade for a grail soon after. But living in the UK I'm not sure how many instant-grail pins you're going to have the opportunity to get. The paris Tangled event for example would help with grail questing. But other than those rare few releases it's what do you have to trade and how much money do you have. Once your traders run out it's all about the money to either buy more traders or buy the pins you want. So just be careful.