Besides, I've noticed that the caloric burn that MFP usually estimates is generally off. It seems to overestimate how many calories burned. I compared the results a few times, looking at what the elliptical or treadmill at the gym told me vs MFP. Since the gym's machines take into account heart rate, weight, age, etc, I'm thinking they're more accurate.

If you're at a drastic deficit, I would eat back calories, at least part, depending on how you calculate them. HRM would be the best for a legit calculation. But, since you're training for a half-marathon, I would probably drop a deficit, eat at maintenance, and follow your hunger, making sure you're hitting your protein macro solidly... Depending on how soon your half-marathon is, you may have to carb cycle if you don't have time to fully keto adapt before your event, because it will affect your performance. But you will get the optimum performance ONCE you are keto adapted, because you won't have the carb-related fatigue many runners get....