Regarding moving the split to full sized deep rather than a nuc, you might consider what I have done when I have an under-strength colony for one reason or another: I position however many frames I plan on using in the center of the box and then add solid follower boards outboard of that and fill any remaining space with foam insulation boards cut to fit. (I put little T-shape "ears" on them so they sit on the frame rest, but sooner or later they break off from the foam, not, of course, from the solid wood follower boards.) When the colony or split grows out of the space, it's simple enough to remove the foam, move the follower boards outward and add in some empty frames or foundaton, etc. Eventually all that is left are one or two follower boards, which are then removed and you're done.
I tried this late last fall and wound up overwintering a colony on a scant 7 frames divided between two deeps. The bees did really well in their cozy, custom-sized space. I was worried it would be complicated to reverse in the spring as I planned on adding foundation-less frames on the sides of the brood nest as an anti-swarm technique. In fact, it was easy as pie to re-arrange when I needed more room for the expanding brood area and the colony grew steadily outward (and upward it's now in four deeps and going gangbusters.)
When I had a chance to make some splits/nucs this spring I re-installed the follower boards (both wood and foam) in some regular deeps to exactly fit what the colony needed and I had available. They have grown out nicely and all I have left in the last deep are two wooden follower boards which I will probably pull in another week or so.
The bees seem to me to benefit from having constantly right-sized cavities and not having the upheaval of being moved from one box to another. The fewer times you have to do that, the fewer chances you have to accidentally damage the queen or create some other kind of a problem.
The follower boards (and the foam panels) are cut to be the full-depth of what-ever size box I'm using, with no shortening to allow for bee space between boxes to keep the bees from having much access to the foam. I have read here of report of bees chewing the foam material, but so far in both cold and warm weather I have not seen that. I have used both Dow (pale blue) and Owens-Corning (pink, and now ozone-safe, light purple) foam boards.