Depending on the density of the hardwood you are using, the coarse-thread screws should work. However, it could cause your material to split. A safer option would be to set the jig up for 3/4" material and then use the 1 1/2" fine-thread screws. This would give you the most penetration while using the fine-thread screw. If you have any additional questions please let us know.
Screw wax goes a long way in hardwoods. Don't ask me how I found out!! LOL
If wax is not available, try rubbing the screw-threads through a block of soap each time for lubrication.