I'm not sure how these things help because I seem to be able to come up with alternative explanations that are not explained by charge. I also don't understand why the lower level orbitals are raised up in energy for the case of acetylide relative to acetone (or acetylide relative to acetylene, also), but not when comparing the allyl anion to the allyl cation. Acetylide compared to acetylene, and acetylide compared to acetone, seem to contradict the comparison of allyl cation to allyl anion.
Acetylide ion has a non bonding orbital that acetylene lacks, and so it is going to have one orbital that is higher energy for sure. It also makes sense that acetylide would have mostly higher energy orbitals than acetone, but that could be explained due to the lack of an electronegative oxygen, which raises up the energy of the orbitals for that reason.
Also, there is a separate thing that makes a chemical reaction go faster which I think is separate from MO energy levels: electrostatic attraction between negative charge on acetylide ion and partial positive carbonyl carbon.