The idea of building F2L except for 2 cross edges, then inserting them with <M, U> and then doing last layer has been suggested before, with different methods for reaching this cube state and dealing with LL afterwards. To reiterate what most people think about this idea: it's pretty inefficient to insert the cross edges with M and U moves and then carrying on, it's probably better to use LSE at that point.I randomly created this "method" when I was high on multiple medicine when I had the flu. I just thought of it and tried it out.
A more promising idea that I was playing around with at one point that follows a similar vein of thinking is to insert two U-layer edges into the DF and DB positions, like what you have done, but to specifically place the UL and UR edges instead. Simultaneously, edges are oriented while you place the edges, so you essentially make a pseudo-EOLine. Then you blockbuild the left and right blocks as normal. Once you get to LL, perform COLL and then you reach a cube state where you've skipped 4a of Roux LSE and setup to finish 4b extremely quickly because the corresponding edges are already setup at the bottom and are only an M2 away from being solved (+ maybe an AUF). Then all that remains is 4c which can usually be done quite with less moves than EPLL. The movecount should be quite a bit lower than your suggested variant. Again, I'll just emphasise that what I've suggested is nothing groundbreaking and has definitely been considered before, but I thought you may be interested in it.