Habari, bwana... The border crossing situation changes often, but Namanga is the one that is always open - I've also crossed at Taveta, if memory serves, and I do know folks who have crossed into Tanzania for a day's drive after a "gift" of a case of Tusker to local officials... but... (I also crossed "extralegally," shall we say, swimming Lake Chala with a couple of friends, Kenya - Tanzania - Kenya, but this is NOT recommended, and crocs have been found there as well; almost got it from a hippo exloring an area adjacent to Tsavo for walking safaris on that same trip - that's another story!)
It all becomes easier if you put your group together and deal with a local org to cover it. We actually had someone from Tazania Sengo Safaris - most of the staff arenow part of locally-owned and reliable
Swala Safaris) meet us at the border and did a portion of our Tanzania safari with them. Swala has tented camps and they know where the game is...
You are quire correct, in December, the migratory game are in Tanzania, not in the nothern sector (Masai Mara) in Kenya. Not that there's no game mind you... Tazania and Kenya are quite different for game viewing - Tanzania is much less crowded, for one, unless you go out of the way in Kenya or stay at a private reserve (expensive.)
(Ah, you got me started! I used to be an Assistant Sysop for Africa and South America areas on CompuServe's Travel Forum - those were the old days!
Drink an ice cold Tusker for me...)