So first off, it is nice to have another person on here who does contact staff. I have been working on transitioning a lot of those moves to saber with varying degrees of success for the last year or so. As to reverse grip, I have a few videos on it but they are old ones. The primary person who used it was a guy named CH3M15T, unfortunately, he does not show up on the forums a lot anymore. His channel can be found here though.
www.youtube.com/channel/UCwiHzcMCb8ZLLlSWd_iMdGgI have a discussion about it here as well
Though I don't spend much time in reverse grip, I do transition in and out of it a lot; these transitions I think are the crux of your question. Basically I have found a few ways to get there.
The simplest is a hand pass from one hand to the other with a half rotation of the saber so that it ends up in the off hand in reverse grip. It can then be passed off to the dominant hand keeping the reverse grip.
The second way (which is I think what you are talking about) is to do half of palm spin. This is quick and dirty with no hand switch needed. Just open your hand, press your palm against the spinning saber, let it go a half rotation, and close your hand. If you do this repeatedly with both hands, it actually has a very interesting look. It is slow and odd and looks like this
The next is an assisted hand roll with a switch. see it here
and here
The next is a flip version of the same. Here I use a hand pass and a 1.5 flip to reverse the grip. This video is the close version. You can loft them a couple feet in the air to do the same thing.
The final is just like the last but without the hand switch. This one needs a bit of air space.
www.youtube.com/watch?v=N9ryhBmoZP4 (Embedding disabled, limit reached)
These are what would call the basics to the intermediates. You can also do a halo 360 or some other complex contact moves like a neck wrap and arm roll to do the same job. I have videos of those but don''t recommend them. Hope this helps.