Advice needed on cutting wood

In my current puzzles the orientation of the grain really doesn’t matter. Well, in one puzzle it does play a role in the assembly, but you haven’t seen that one yet.

However, I have a couple of other items in mind that the grain does matter. Well, at least the difference between end and face grain. This is important because it matters on how I can most efficiently cut these out.

Here are a couple of examples of what I mean:

Cook's Pushstick

Stars Puzzle

In both of these items, the side that is facing up should be the face grain. However, I really don’t want to cut out a lot of individual pieces if I can help it.

For the Cook’s Pushstick (used to push a hot oven rack back into the oven using the end slot or pulling it out using the side hook) I can see drilling a hole in the end and then cutting a slot using the bandsaw or a dado set. Then setting the resulting stack on it’s side and slicing them off to the right thickness.

The same sort of issue with the puzzle pieces. You want face grain showing, not end grain. However, how thick can you usually get “exotic” woods? Especially without going over budget buying that sort of wood.

Thoughts from the more experienced among you will be greatly appreciated.