04 V6 Rumble/Vibration

Hi,
Take it to a tire shop and have it aligned & the tires dynamically balanced. AM only does a static balance of their Tires/rims. Their sticky weights are well known for falling off in transit. If there’s a brake dragging or air in the system a vacuum bleed should take care of that. I’d look over the suspension components, ball joints, springs, any interference, loose fasteners with the car jacked & on stands firmly on the frame.
Can the vibration be recreated when the vehicles in neutral at a few thousand RPM‘s? Feel it in the steering wheel? You didn’t mention if it was an automatic or standard transmission. It could be a broken pilot bearing if not an OE replacement or the transmission was incorrectly aligned when the car was reassembled or the clutch was not replaced with a quality unit, or installed/broken in incorrectly. It may also be the Throwout bearing riding on the fingers of the clutch, was the clutch ever replaced, if so- with a quality unit?
Have a firewall adjuster, or quadrant. If an automatic, it may be a flex plate crack or torque converter fasteners Loose, notorious for such without a form of non permanent Loctite.
My first step would be to ensure the tires are correctly balanced. When removing a driveshaft it’s important to reinstall it to the same bolt holes as originally installed. Perhaps the driveshaft is out of balance or a CV joint is on its way out.
Pick the car up and look for loose Bellhousing bolts & other issues, e.g. transmission mount separation or loose or broken fasteners.
You can verify it’s not a belt driven accessory by removing the belt and checking all your belt driven accessories that there isn’t a bearing or idler issue, harmonic damper falling apart (all Modular motors are internally balanced), alternator, AC unit, (the feeling change with the A/C running or not?). There’s no one single answer, you need to verify whats in error by jacking it it up, may seem like the drivers side, but hard to pinpoint as suspension requires checking things one by one, putting on stands, looking closely for an issue, listing a more detailed history of the car will likely yield a more accurate response. What point did you realize the vibration, what was the last thing done before it was noticed?
Are the lugs bottoming our on the Rims, are the tires rotation arrows in the correct direction(s)? (it happens).
Best of luck, with a little. effort, I think you’ll locate the issue. Feel free to ask questions if you have others.
Good luck!
-John