We went through the same thing a few months ago. DD6 was splitting her day between kindergarten and 1st grade, and at first loved it. But then, got more and more frustrated for the same reasons you mentioned - the kindergarteners were getting to play and she wasn't. She also was starting to notice that she didn't really feel like she belonged in either room anymore. We ended up moving her full time into 1st grade mid March. (She too is doing 2nd grade work in 1st grade, and could be doing more). When we asked her about the idea of moving up she loved the idea, because then she would be doing the same as everyone in a room again.
It has worked out really well and she will be going up to 2nd grade next year, with another possible mid year skip if we need it.
I have had lots of thoughts of whether or not I'm "cheating" her out of things from kinder, but she is so much happier now in 1st than when she was splitting that I've finally accepted that she really wasn't being cheated out of anything.