You need some separation between the halves or it won't have any clamping force. Dave's blocks are made to have an 1/8" separation. You won't crush the tubes under normal clamping pressure. Your band saw blade may not even be wide enough. Of course I would skip that step (if buying new wood) by putting two thinner halves together so they wouldn't need to be split apart.

Mahogany would be way down my list of wood choices although it will work. Of course if Pete has some handy he won't have to be bothered running to the store. I made a wood block out of it one time and it was not very durable. My hard maple blocks I made 34 years ago have lasted much better than other woods I have tried.