According to the information about the UniTak3D direct drive bracket it is supposed to work with all extruders, including the BMG. I have a BMG and other than possibly printing a mount, the UniTak3D is at the top of my list.
As far as your temperatures go, have you done a PID tune of your nozzle and bed? I am printing eSun white PETG at 235.
Also, a great bed surface for PETG is a PEI sheet or PEI flex plate. I personally like the PEI sheets since the are a bit thicker and to me seem more durable. You can even scuff them up with fine steel wood if they start getting slick. I use the Gizmo Dorks PEI sheet and just applied it to the plain glass side of my bed.
One note - my Ender 5 is one of the originals with a 1.1 board - the pro comes with some/most of these upgrades at this point. Minus the PEI bed and ABL - which is simply super good, too good to give either up. By the time you add all the upgrades to a base 5, or add the missing ones to the 5 pro you can pick up a 5 plus. At the 5 plus price you're getting closer to prusa pricing -$200. Speaking from experience my Prusa required A LOT less fiddling to get it right. Almost straight out of the box good printing. ($200 may/may not be a deal breaker for some so just throwing that in here) Now to the point.
The few upgrades I've done which seemed to really give a quality of life improvement for my printing was purchasing a PEI plate for the bed, an EZABL sensor kit for bed leveling - trust me it doesn't take a rocket scientist to learn how to level the bed, but on this printer with stock setup doing it all the time gets really old (also picked up their solid bed mounts), and you will be doing it all the time because the springs will not hold the bed position, and last but not least get rid of that plastic extruder and get yourself a metal one!!
After the first two my print quality and QoL was so much better and easier to tweak on. The third one you'll end up doing sooner or later because it seems just about everyone's stock plastic extruder ends up cracking. The last upgrade I'm going for today actually once my parts arrive is the silent board (check videos out after hours of printing you'll want on too if you're in the same room lol) and the capricorn bowden tube which I'm not totally sold is needed since I mainly just print PLA - but figured I may as well for $8 give it a try.
This is the 1 I am currently using and you can always go this route to refresh whatever build plate you have if you want.
Get an oversized one from Amazon and trim it to size. While you’re at it get a pei one - those are amazing.