Thanks for the suggestions. I'll try to address everything in one message. Pulling in forward is really not an option because my wife is terrified of going on the foredeck, and doesn't want to take the helm. Backing in allows us to grab the spring line from the cockpit first, and once that's secured I leave the helm and go to the foredeck to do the rest while my wife secures the rest of the lines at the stern. There are also other reasons related to the boat controlling much better in a cross-current when pulling through the fairway in reverse - I thoroughly covered that in another thread last year.
The suggestions about turning the rudder (and motor, since I have a really nice hard link) with forward and/or reverse thrust did not seem to work to move the bow closer to the T-dock. The current was just too strong. I think the keel is broaching, as Denise mentioned. Crossing the stern lines is a problem because I raise the outboard, and the lines can get caught in the prop and/or rub through the paint on the lower unit (I've had both happen on my powerboat before.) The bow is narrow, and the cleats are so close together that crossing them makes no difference except to increase chafing. Fortunately they are floating docks, so we don't need as much slack in the lines, which is another common reason for crossing them.
All this may be academic anyway. I think I'm going to move back to the slip I had last year. I was at the dock today in 17 kt breeze, and not happy with the way the boat was bouncing around. Also, way too much driftwood all the time - you can see in the photo that there's an open fetch and the flood current just pushes all the crap right into my slip. In theory, the ebb should push it back out, but instead it creates a logjam behind my transom and collects there. The brand now paint (Pettit Vivid - a hard paint!) wore off the trailing edge of the rudder at the waterline after only a week!
Also, there's a guy next to me on the outside of the T-dock who's a total a$$, has complained about everything from the position of my shore power cable to the location of my cleats (as if any of this affects him) ,and I suspect he disconnected my shore power the other day to get under my skin. I've never complained about the huge dock box he put at the end of the T, which he obnoxiously located on my side so I can't get to the cleat if I put it on the end of the dock. (This box is clearly visible on the satellite pic above.)
Much as I like having a T-dock for the length of my boat, my old slip was much better protected from both weather, current, and debris. The guy who was in my slip last year left because of a dispute with a neighbor, and I think I've learned the hard way who his dispute was with.
This pic (oriented north-up) shows both my new slip and the one from last year: