It should not take 2-3 revolutions to shift modern chainrings. There are possibly a few things going on.
- Your larger chainring does not have the pins and ramps required to shift quickly.
Sometimes cross sized rings don't have all the bells and whistles.
Your big chainring should have those features. If it doesn't get a new ring.
Race Face and Black Spire make 110BCD rings with pins and ramps in cross racing sizes.
- The derailleur needs adjusting/replacing.
The derailleur cage needs to be positioned such that it is about 2-3mm above the big chainring. The cage also needs to be curved such that it closely matches the curvature
of the big ring. 46t is right at the size where a standard road derailluer has problems.
It should look something like this.
If you can't get the derailleur close on both top and bottom, you can either get a cross specific front derailleur, or grind the cage of your current derailleur to match the curvature of the big chainring.
- Your shifting technique needs practice.
As someone who learned to shift before indexing, I have some habits that I only recently learned modern beginners often never learn. Even with indexed shifting, on the front you need to push the lever beyond the click until you hear the chain catch. This is something I was doing unconsciously since that's what friction shifting requires, a slight overshift and trim. Recently in helping a beginner learn to shift, I took a closer look at what I was doing and they weren't and realized that they let go of the lever as soon as it clicked, not as soon as the chain engaged the big ring. This makes a big difference in how fast the chain shifts.
They also needed to learn the subtleties of soft pedaling during the shift.
Modern chains and rings have gotten so good that in normal situations ( 39/52 on the road), you can often go a long time before these tricks become unconscious. Cross racing is tweaking the boundaries of what the shifting system can do for you and requires learning these old school techniques.