Oh very clever on how you attached the LED strips in the cabinets. Why didn't I think of that?! Well, on the other hand, my rope lights were kind of "sticky" (in a deteriorating plastic sort of way) so I kind of wanted them out. I would definitely have tried your idea if I'd seen it while the rope lights were still in place though.
I guess you won't be forgetting those cabinet doors open!

(I always found myself doing that with the old, power-sucking dim rope lights).
By the way, if a person prefers, those LED strips are also available in a warmer white. I bought a roll when I was considering using them (eBay). I find that something around 2800 to maybe 3400 Kelvin is warmish, then 4000 is whiter, and 6000 or so is the "blue white."
I like the lamp. I converted an IKEA table lamp I like to DC/LED, and it is kind of a fun "house like" touch vs. all the vehicle style lighting; but I have to remember to put it on the chair when driving, and it does take up table space. Also blocks the hummingbird feeder view if I forget to move it. I like your idea as it kind of takes the best of both.
On the off center hole: If your upper cabinets were made anything like mine, it's not TOO bad to get to the wiring and I think maybe you could then put the lamp on center with the base just covering the off-center hole. Maybe you already know this and there is some reason it can't work... Or yours are different... But anyway, the way my upper cabinets work is this (going on memory here, so hope I have the order correct):
1) Pry out inner/end carpeted piece.
2) Pry out back (outside wall) carpeted piece.
3) Lift up bottom carpeted piece.
These all (except maybe for #1, I forget) have some white, washer headed Phillips screws holding them in place (I guess they don't make those in Robertson drive

). They are all easily visible on my rig.
Behind #2 is all the wiring that runs fore-and-aft.
Under #3 is all the wiring for the "overhead" lights on the cabinet bottoms, the 110 outlets, etc. The false floor has a fair bit of space under it (because the speaker backs stick up some inches and they are under it - at least in the Concourse).
So - at least on my Chinook - if you had panel #3 lifted up (I prop it up with a screwdriver to work under it) you could just make a new, centered hole, and run the wire through it. I wonder if it's the same or similar on yours?
Edited to add a couple of photos:
This first one shows the basic idea of the various carpeted panels I described above. At least in a '99 Concourse. In this one we're looking into the cabinet over the kitchen sink. The "wall" on the left is the one that is common with the shower.
Here it is with the "floor piece" lifted up. The whites are the bundled (chassis) grounds. The 110 wiring is the Romex style wires; the others are DC. The bundle on the lower right is (although you can't see it very well) going out a small hole to the Thin Lite over the sink. There are multiple wires because it continues on to the other Thin Lite over the couch, etc.