Have you tried editing the playlists to point to the correct location before importing them? If it's a simple text replacement it shouldn't be too complicated a task.
Find What: D:\Music
Replace with: D:\Music\Music
Of course, if some of them already say D:\Music\Music you're going to wind up with some messed up entries and you're going to have to account for that. Maybe first a replacement from D:\Music\Music to D:\Music to get everything in the same state, and then the final replacement. Logic it out.
The other option, maybe the easier one, is to move your music files from D:\Music\Music to D:\Music (with the rest of the structure in tact) from within Musicbee, and that way your library and your playlists will agree.
I'll admit to being very curious as to why, when setting up your new system with all options available to you, you chose to put your music files one folder level deeper than they were one the old system. Why not just put them in D:\Music from the start. Not that it matters now, of course. I"m just curious.
All the best!