It's at least partly your body telling you that it wants those carbs back in it's diet

As I've beared down on the goal of eating three meals a day and cutting carbs to a third or lower of what I used to take in, I've noticed that I seem to get hungry more often, and the pangs are a little sharper. Can someone tell me what's going on?

It's at least partly your body telling you that it wants those carbs back in it's diet. Our bodies like the feeling it gets when we eat carbs and have lots of blood glucose (bg). In short carbs, particularly the high GI (starchy) ones are addictive and you are in a real sense suffering withdrawal from that addiction. That will abate with time.

Going full-blown low-carb can condition our body to not expect those carbs and the hungries will go away in a fairly short time if we're eating sufficient protein & fat. Half-way measures, i.e. modest carb reduction, still teases the body with some quick bg and so it continues to crave more which manifests as hunger. Then---When cutting back on carbs, we need to eat sufficient protein & fat (unless making supreme effort to lose weight and even then ...) to provide the energy that we're not getting from the missing carbs.

Protein digests & appears as bg in about 4-5hrs so that will provide you some energy after that supplied by the carbs you do eat has abated. Fat slows the digestion of the carbs you do eat and thereby allows those carbs to feed your body albeit at a less bg level for a longer time between meals. I'd suggest a small low-carb snack with some fat & protein when hunger pangs strike. "Tree nuts", cheese, etc. I like chiccarrones (pork rinds fried) which are very low-carb but do supply some helpful fat. Sometimes I eat them with an LC dip of some sort.