Taking the analog plunge...

Does your 5i have a phono stage? This is the only piece that you have to worry about matching with your gear. If not you better plan on budgeting for a VK-P10. Even used that will eat a big hole in your 4K. Ofcourse you don't have to stay with BAT. You could pick up something like an EAR 834P which will work well with your 5i. That would leave you with about 2700 to 3K for the table, arm and cartridge. You have a broad selection of good performing cartridges at or below 400. So that puts you around 2300 to 2700 for a table and arm combo. There are lots of great table/arm combos out there in this price range that will sound great with your BAT gear. You just need to do some research here and over at the Asylum. Keep in mind that it makes more sense to put money into the table first and then upgrade the arm and/or cartridge latter. Don't discount buying off the used market. I'm on my third table bought through the classifieds here on A'gon.

Thanks for the advice Dan. No, the 5i hasn't got the phono stage. I've given thought to the P10 and balk at the idea of spending 3k for one. It's odd that you mention the EAR. My search began with the 834P and I was very encouraged by what I read.

I definitely have no qualms about buying used and have done so over the last couple of years. Outside of that, I have been impressed by J A Michell. The build quality looks quite good and the chatter I'm hearing is equally impressive. I have no idea about cartridges at this point.

FWIW check out the Nottingham line of TT's. I'm impressed with the design of the Spacedeck and Arm and the user reports have been very favorable. This will probably be my next table. Others here recommend Teres a lot. Then there is always VPI and their endless (seemingly) upgrade path.