Thank you Marik for your listening and your comment. I was trying to get the sharp attacks that I hear in many modern classical piano recordings. But I think that you may be right.
I'm not ready, and anyway would not be allowed, to transform my living room in studio. I could possibly put bass traps in the room corner where is the piano, but certainly nothing on the ceiling.
A possible advantage of LD is that at close miking the sound is less peaky than from SD. I did another take with LDs a bit further away just outside the piano. I think it's better.
For less than perfect room conditions I prefer MS. Mathematically it is equal to XY, but has a few major advantages: 1) The "M" is pointed directly to the source, eliminating most of the room influence, 2) Later you can manipulate with the "S" channel separately--use an EQ, reverb, etc, removing resonances and peakiness, and adjusting the "room" sound, 3) Change the width of the stereo image to your liking in the post production, and 4) The microphone positioning is somewhat less critical, but still generally, in most of the cases I prefer at least 1.5-2m away, somewhere between a stick and beginning of the curve.
For the "S" I use ribbons only, which have much better fig.8 pattern and limited directivity in the vertical plane, eliminating a lot of ceiling and floor reflections. Also, their (generally) limited top frequency response helps to eliminate room "ringing".
Since you have two 4038 I would not be afraid to try Blumlein either--something what ribbons do a marvelous job. Each room is different, but with the right mic technique and right choice of microphones it is always possible to get a decent sound even in a very bad one.