@qw098
This is why I don't like it. A proton has a small charge and while it can attract electrons, it is difficult to attract two pairs of electrons. When two pairs of electrons are attracted in a hydrogen bond, the angle is usually 180°. That angle allows the electrons to not repel each other.
There are intramolecular reactions with smaller angles. The decarboxylation of a beta-keto acid results in a proton transfer in a six-membered ring. An elimination of an amine-oxide, sulfoxide or selenoxide involves a proton transfer in a five membered ring. Those are the smallest bona fide examples that I can find.
You could draw your tautomerization with a water or alcohol molecule to make a six-membered ring, but this would increase the entropy of the transfer. If you are in a proton medium, it seems likely that proton transfers can occur with the protic solvent. Perhaps you could think of this analogy. If proton transfers in the NMR are so rapid that the splitting from adjacent protons is not found in the spectrum, then you could expect that proton transfer without tautomerization may also be a fast process and protonation on carbon may be a slower, but thermodynamically favored reaction.
Secondly, you should make a model so you can examine the actual distances though which you are transferring the proton. You should also remain aware that the alkene electron orbitals are perpendicular to the double bond and the proton must reach them.