I removed the quarter round and two trim boards to install a new hardwood floor.  I partially split one of the larger (lower) trim boards.  The split is about 24" long.  The wood is 12" wide birdseye maple in 14' lengths.  So, it is not replaceable at a price I can afford.  I would like to repair the split as best as I can.  Do not need structural strength here, just a good looking finish.  I would prefer not to have to refinish the board.

My current plan is to carefully open the split a bit wider and using a toothpick work in some good quality carpenters glue (Titebond III seems highly regarded around here) then clamp.

Do you have a better technique?  Any tips?