Interesting... It's definitely a vibration, as opposed to something interfering/touching. I'm stock emissions wise so there's plenty of downpipe clearance. I'm also stock with regards to engine/transmission mounts with the exception of the insert.
I had zero NVH issues prior to installing the insert. Besides the typical, but minimal, diesel engine sound there was nothing to note in that area. How would my engine/trans have become misaligned and what exactly do you mean by misaligned? Would you suspect it happened during the install of the dogbone insert?
If not during the installation of the insert I would think I should have had some minor NVH issues before, that are now be amplified by the insert. That being said, I also suspect the stock motor/trans mounts would be relatively soft, especially on a diesel.
To be honest I don't expect anyone would find the vibration I'm feeling acceptable. I'm more eager to pull the insert than my wife. Part of the reason she agreed to switch cars with me is so that I get a break from turning wrenches. I tried to explain to her that pulling the insert will take me something like half an hour start to finish but she was having none of it. At the same time everyone says not to get an insert on a diesel. No other user reports until yours to compare to so I figured everyone was right... maybe not. I would love to keep it but the vibration is a no go. It also resonates when the windows are down, downright unbearable.
I had a 2010 Mk6 TDI /6MT that I put a BFI GTI dogbone insert in a couple months after I bought it new, it added a bit of vibrations, and within a week they were mostly gone. For the next 70k miles I drove it until VW bought it back,there was nothing more than the feeling of a clickety diesel engine, which is to say you wouldn't confuse it for a gasoline engine, but it wasn't anything like an old Mercedes.
With my current 2015 TDI /6MT that I bought used (w/ 60k miles, bone-stock), I installed the Powerflex insert, the euro short shifter and the solid cable bushings, and I put on Golf GTE front calipers (same as the non-PP GTI, but painted blue instead of red). A few weeks after all that I let its old owner have a spin in it (he's a bit of a TDI nut, he owns another 2 TDIs) and he noticed the shifter, definitely the brakes (going from 288mm discs and 55mm piston to 312 & 57 is a huge improvement in brake feel), but he didn't notice any NVH from the insert, even after I told him about it.
Both in the old Mk6 TDI and in my 2017 GTI I could sort-of make out a bit of vibrations from the BFI dogbone inserts, if I really focused on it (the GTI doesn't have the insert anymore, as I said in my previous post), but the Powerflex in my current TDI is not noticeable at all.
When I changed all my mounts on the GTI, I started with the engine mount (not ideal, but it's the easiest one to replace and I didn't have much time that day). Because I rushed it, the engine got slightly misaligned which caused some NVH, especially when starting from a stop/engaging the clutch. I believe the BFI insert that was still present at the time caused the engine shift when I replaced the engine mount. The next day I got the car on the lift and looking up from under the car I could see the engine was not perpendicular on the car's front-to-back axis. I had to loosen the 2 front dogbone arm screws,the engine mount screws and have a buddy with a prybar leverage the engine in place while I tightened the mount screws, then the dogbone arm and the big dogbone screw (the one going through the mount & insert).
You can read through this thread, Twist has a good explanation on the engine alignment, since he's done it a bunch of times
https://www.golfmk7.com/forums/index.php?threads/bfi-stage-1-engine-tranny-mounts.356688/page-3
Watch his video on page 6 in that thread.
I gotta change my oil probably next weekend and I can take some pics from under my TDI if you want to maybe compare with yours. Let me know.