The reason that broadheads behave differently than field points, is that they have more cross-sectional wind resistance.
Cross-sectional wind resistance, is one of the forces that allows fletchings or vanes, to stabilize an arrow.
A broadhead, acts like vanes, on the front of the arrow. If you want less deflection from crosswind or poor tuning and rest placement, you need to look for broadheads that have less cross-sectional wind resistance.
In other words, they need to be smaller.
If you insist on shooting large diameter heads, you need to give the vanes more ability to steer the arrow, so they need to be bigger as well.