I've had some interesting experiences with Time Machine. While you're using the machine, it tends to take a back seat. The VERY first backup takes forEVER. (The Sandlot: FOR... EV... ERRR). But once you get past that initial backup, then you're good and they're usually fast. Any disk io will be preferred to time machine. It goes a lot faster when you're not using it too.
I bought a 4TB disk from Amazon that was defective from the moment I got it. Should have returned it but I stupidly decided to take it apart to see if I could put it in a different enclosure - the microUSB was the board, but the drive transferred slower than anything I've ever seen. Even though I bought my wife the same drive, her drive was perfect, but mine was slow as heck.
I have a 2TB WD External that overheated in a zipped container - ever since then, it transfers at USB 2 speeds and refuses to go faster. :/
My MacBook will backup to Time Machine when it's in a locked state - so I suggest setting that overnight, and let it do its thing.
Another thing you might try before taking on more extreme measures is running the Terminal command that disables throttling for Time Machine and speeds it up:
sudo sysctl debug.lowpri_throttle_enabled=0
Usually, Time Machine is deliberately slowed down to an extend where it doesn't affect the performance of your machine, but if it's being too slow, then it can be desirable to disable that behavior. This will make Time Machine more of a performance-hug, so it may slow down your machine slightly for the duration of the backup, but if there's any issue with the throttling process or if there are any other processes that hug your CPU, this should solve it.