On that note, a cool trick is to go into the clip tab in mocha and adjust the color space, gamma, etc. The clip tab color settings occur first in the stream, so it will influence the tracker, no need to render.
That said, it is extremely rare that I use this technique.Â
Hey if the shot is over or under exposed there is a trick I use to give mocha more tracking info - We were shooting very flat ARRIRAW 4444 for a project and I was having a really hard time tracking a few shots, so I re-rendered the footage with the LUT baked in and majorly boosted the levels contrast. When I ran the footage back through Mocha it had a much easier time locking on to the plane edges. Then I just applied the track to the original footage and it worked great. So try adding sharpening and balancing the  histogram, and re-rendering just for the tracking bits, it could help. Unfortunately you do have to render it first, as mocha will not pick up any AE filters just applied on the timeline
I would personally recommend avoiding green and simply have the device set to display a medium/dark grey screen that will show "some" reflection but also give you visual reference of the screen edges against the black border. In general, if you track the edges and avoid the actual screen, mocha should be fine. Also note, placing small white dots on a black screen is not necessarily going to "help" mocha. mocha's planar tracker is looking for texture. So if possible, use a pattern and not a "round, white dot".Â
Here is a link to a free 1.5 hr training webinar that specifically covers using mocha for difficult screen inserts. I would highly recommend this to any AE artist that has used mocha for the basics, but does not fully grasp some of the more advanced techniques for avoiding reflections, handling the really difficult tracks or the AdjustTrack module.Â
We use small tracking target stickers at each corner of the screen and mocha takes care of the rest. How experienced are you with mocha? Even the most difficult tracks can be accomplished manually but there are a lot of ways to do it you may not know about. There are some great advanced tuts online even pros could learn from.
We never use green because as you said it blocks reflections, but more importantly you can get green spill on the actors that is harder to manage.