Warmoth has two peghead hole sizes - for 3/8 posts and 11/16 posts. Figure out which one you have (or ask Warmoth).
I'm not sure how they "tilt down" to the bridge under tension - the Schallers I have lock to the peghead with 4 small screws and they don't tilt, no matter the hole size. The correct hole size is good for making sure the bushing fits and that all of the machine heads line up correctly.
Schaller machine heads are generally the "big" ones though, so I'm a little surprised your others are too big. Unless the warmoth neck is drilled for gotoh or ultralite small heads.
See this thread:
Measurement for tuners