Assembling a substructure piece of a current project I broke three screws. The only way I know to recover is make new pieces.
This was using white oak. Should the holes be pre-drilled in piece "B" before driving screws?? Never had to do this with red oak or soft maple.
Depending on the density of wood you are screwing into it can cause additional issues with joining your material. First off I'm assuming that you are using our fine threaded screws since you are working with hardwoods. If this is not the case that would be your main issue.
With harder words like this the best technique is to drive your screw part way in and then back it out some and continue this process until the screw is all the way in. This will allow the threads of the screw to be cleared making it easier to drive. Another tip would be to coat the threads of your screw with beeswax or paraffin wax to lubricate them going into your material. Using these tips you should be able to have success with this material and our screws.
When installing screws in hardwood, I use "screw lube", and don't have any issues with screws breaking.
I work a lot of hickory and on occasions a screw will break off. It is not as common in installing a screw as it is when removing one. What I have is a small 1/4 inch hollow screw extractor of which is actually a small shaft of steel with teeth cut in the end. The process is quick and easy and how it works is by cutting a plug of wood from around the screw. Once drilled down below the length of screw, pop out the wood containing the screw and then plug the hole using a 1/4" dowel of either the same species of wood or even just a plug that you glue back into the hole. They are similar to a hole saw only longer and smaller. It is a cleaner looking and easier repair than drilling a series of holes around the screw using a 1/8 dia bit, popping out the wood with the screw and then re-drilling the area with a larger bit and then plugging it.
These are available at some woodworking specialty sources and come in a set if 1/4- 5/16 and 3/8 and or you can make one using a thin wall tubing of which you use a file and cut teeth in them. They are not cheap however worth their weight in gold once you need one. You save the cost on the wood that you have to replace and sometimes it is not possible to replace the part. I think I got mine from Lee Valley Tools but it has been a good ten years agoi. I have used them several times on dis-mantling of furniture as well as cabinet modifications.
Kreg has also changed the screws. It is my understanding, and I could be wrong, but the older dark colored screws had a dry lube on them and the new bright screws do not.
Hope Kreg will chime in and either verify this or say it isn't so.