Without researching the product's specifics - sounds to me like you need a new angled upward stem instead of more spacers.

However, if a bike has a short stack, then usually, the head tube is shorter.
Given the same stem (which is likely an impossibility across brands) the shorter headtube results in a more aero position.

So one question is: what does the stem do for hand positioning? Relative to your other bike choices.

And, if you upsize for more stack, is the reach close to the same? ...or made close with a simple stem change?

There is often more than 1 frame size that achieves a fit that meets your needs. Given your wrenching ability to swap components.
Or.
Maybe start with a good fit on the bike, by an educated eye.