When I had a chef table in my kitchen at the country club I considered it a honor to do the menus and to be honest it was a ton of fun.
The service staff should be doing all the presentation.
Do the tasting menus, make a name for your self, and leave tips to the service staff. Your financial reward comes later when you can demand much more than a server could ever make.
In my neck of the woods, Chefs Table, Tasting Menus, etc. are usually a group of people who somewhat understand food. (Foodies). Usually the bill will require a percentage tip for that number of people. The group will usually decide to tip the FOH above percentage if they had great service, and they will also decide to tip the BOH if they had a great menu and food.
I would never consider dividing tips unless the FOH provided only beverage and the BOH took care of service which is pretty popular here. Usually there is one back waiter for removal and a Sommelier for pairings and pouring . The food is plated and served by the Chefs. The group will leave two tips on the bill. It's that way because cash is not popular here. Someone usually throws the plastic.
Forget the tips. A good waitstaff who supports your efforts deserves the tips. Everything you describe having to do is part and parcel of the tasting menu concept. As Lagom points out, this should be a lot of fun and a welcome break from your standard activities. Don't create an issue where there isn't one.
As Lagom pointed out, in many parts of the US there are laws forbidding managers (that usually includes chefs) from requiring that tipped employees share their tips with them.
And as others have stated, why bother? Your "tip" is the fact that you get to do something fun and outside of what you normally serve. When I've been in that situation, where the table wants to tip me, as well as the waitstaff I always decline, but tell them that if they would like to buy my cooks a round of drinks after their shift that would be much appreciated (and yes I know that there can be issues with that also). The point being that my staff deserves the "little extra" not me.