Tele and Strat bridge installation

Okay, Ive now a Tele and a Strat that need bridge installations. There are no previous holes drilled to align. I've figured out how and where to exactly place the bridges. I am probably going to order a set of deepthroat clamps to clamp the brides down to mark and drill the bridge screw holes.
Now, the problem is that when i mark the holes, and then drill, then screw in the bridges, then the bridge always shifts a little, either to the left or right.
I've ruined a previous installation with the bridge shifting and had to dowel the bridge holes again.
I'm thinking perhaps I should just take the guitars into a professional luthier?
Should I try it again? I'm very much a novice at this.

as long as you mark and drill straight you should be fine. draw a centerline down the guitar.

the strat, if it isn't hardtail, will require a special routing template.