organic chemistry - Is there a way to force C-protonation of an enolate?

In another question, I mentioned that O-protonation of an enolate followed by tautomerization may lead to increased amounts of the thermodynamic product over the kinetic product (when those are different species).

The idea that the oxygen is likely protonated first has been discussed previously.

The way, I think, to get the most kinetic product is to use a bulky acid that would do C-protonation rather than O-protonation (assuming sterics explain the difference in kinetic/thermo product). The proton would have to be a softer electrophile, i.e. less positively charged than a proton from a stronger acid.

To continue with the example I gave in the previous question, I think it's likely that C-protonation would look like this, where the major product would be the kinetic product:

So my question is: are there acids that are known to specifically protonate the carbon of an enolate rather than the oxygen? I was thinking maybe BHT would work. Or maybe the thiol analogue of BHT - yes, it would be more acidic than BHT, but it would also be a softer nucleofuge than the BHT anion. This reasoning works with alkyl halides, i.e. softer leaving group = more C-attack, but I'm not sure if the same goes here.