I am still getting up to speed with the new tuning, but I can already tell by messing around with a simple 12-bar blues that it is making a huge difference. I think the main thing working to my advantage here is that I am learning the fingerboard this time as a musician who has some idea of what's relevant and important, and with standard tuning, I have decades of bad musicianship associated with every chord/scale shape.
With my current practice regimen, I associate sounds (chord voicings, arpeggios, runs, patterns) with each chord tone, so pretty much every diatonic note on each chord means something to me, and I already have some association built up with the fingerboard. I.e. I already feel like I have a more direct link between my musical mind and the guitar.
At least for the one tonality I have practiced so far - Mixolydian.
Still lots of work left to do, but I should have enough to fake my way through an R&B gig by Friday (cross fingers).