Yea keto thrives on fat, you transitioned your body to burning fat almost exclusively for fuel so you need to keep dietary fat up some especially to support high activity levels.
I've been using RFL and UD2 for the past 4-5 months. During the holiday season I was on a home brew diet but before that when I wasn't trying to get fat I was intermittent fasting. I've actually been IFing for years now and use it in conjunction with lyles programs. It works incredibly well for me when it comes to diet adherence.
Anyways I don't think your going to like what I suggest. I think attempting wieght training with 5 days of running on a deficit is the same or worse than running 7 days a week on the same deficit. You're simply not going to recover well enough. Have you taken a diet break? Let your calories come up to maintenance levels for a couple weeks? That could be all you need to make the final push. When I go on a diet break I lose 5 pounds. I guess it's all the hormone levels returning to normal and letting go of water and such.
Also have you thought about getting a Dexa scan? It might be eye opening to see an objective measure of your body composition. What if you were continually pounding your head into a "metabolic wall" because you were near essential fat and your body was just shutting you down each time you approach it. Could be a health concern.
Anyways I say keep carbs low raise fats some and come up to maintenance for a couple of weeks you might find you lose that last bit and have all the energy you need to run everyday. Are you one of those crazy people I see bundled up during the winter months running on ice? Just curious