Cable lighting is usually begun at the wall it just requires electrical placed at the beginning. I use Tech when I want kabel so check out what thye have now for LEDs I do know they have some center feed but I have not used it. I sure would try to use cable in that space . I live in a small town now and my clients tend to be a bit on the traditional style wave so I have not been up to date with all the new form Tech

As Patricia suggested, Kable Lite does have center feed capability:

https://www.lightology.com/index.php?module=prod_detail&prod_id=11574

Your biggest problem, though, will be where to put the required bulky transformer. The transformer is either a surface mount:

https://www.lightology.com/index.php?module=prod_detail&prod_id=71692

or a behind the wall mount:

https://www.lightology.com/index.php?module=prod_detail&prod_id=11489

Obviously, the surface mount is the cheaper option, but can you tolerate a bulky bulge on your cathedral ceiling? With some creative wiring, the surface mount transformer could be mounted near the wall switch (behind the wall in a closet or cabinet??) and the existing Romex used to carry the 12v power up to the ceiling center feed fixture. With an existing 15 amp lighting circuit, the 14 gauge Romex could carry a max of 144 watts of 12v power under the NEC 80% rule.

Short answer yes. its a matter of the right parts.

Thanks!

Follow up question:
Can I have the cables go in either direction from the generator? Like to the left and right?

As you can see from my picture of the power source, it’s not centered on the beam or on one side. I’d like it to go all the way across.

yes.

do you have a lighting store near you? What is your budget for this, have you looked at pricing?