Can I not move a 2 year old time machine backup connected directly from my main computer over to the NAS share?
No... "move" as in archiving a completed Time Machine backup sparsebundle disk image for later use, perhaps, but using a non-Apple NAS in conjunction with Time Machine isn't going to work for a number of reasons. Not only do non-Apple NAS devices not use AFP, their hard disk drive file formats might not be HFS+, a Time Machine requirement.
If you expect Time Machine to be reliable it must be used in accordance with Apple's Time Machine documentation, meaning non-Apple NAS devices are unsuitable for its use. Apple's Time Machine can be used with Macs having directly connected (as in, not networked) storage devices. If they are not so connected, the networked share requires either an Apple AirPort Time Capsule or an Apple AirPort Extreme Base Station. Read Backup disks you can use with Time Machine - Apple Support. Anything else and you're on your own.
Excerpt: "If your backup disk is on a network, the network server must use Apple File Protocol (AFP) file sharing. Both your Mac and the networked backup disk should have OS X v10.5.6 or later."
That's a problem with non-Apple devices not only because OS X is proprietary, so is AFP. Non-Apple NAS devices use a perennially buggy, poorly implemented open source implementation of it.
For that matter Time Machine is just as proprietary and intricately interwoven throughout macOS. Nonconforming Time Machine installations may appear to work, perhaps for a long time, until one day Apple silently releases a macOS update incorporating a change in Time Machine that they never discuss. Hapless users often discover their nonconforming implementation is broken long after the fact. This has happened with disturbing regularity over the course of a decade.
Apple has absolutely, positively, no interest in testing nonconforming Time Machine implementations. That hasn't stopped people who think they know better than Apple from trying to use it inappropriately, leaving them frustrated and angry when they find out it just won't work. To learn how to use Time Machine please read How to use Time Machine to back up or restore your Mac - Apple Support.
