Competing Workout Goals (PFT/half- marathon) Training and Schedule help?

Ok, I've got two different fitness goals at them moment and I'm trying to figure out the best way to go about achieving them/ scheduling them.

Some context: I'm very seriously considering/ planning to join the military (AF). Right now I should hit the weight requirement end of March/ beginning of April and I'd like to feel comfortable officially applying at that point. Right now push ups are a problem and my run time could be better.

I'm also training for a half marathon in March (and again, want some improvement for the running component of the PFT).

I also have a fairly intense martial arts class twice a week for 3 hours.

So my original training plan was full body weight lifting routine (3x a week), running (3x a week) and then the two class generally doubled up on the two lighter running days and one day a week completely off. But especially with having to increase my mileage for the half marathon I was getting really tired and worried about burn out/ not enough recovery time. Especially since I am still in a deficit; I'm already fighting an uphill battle for strength gains I don't also want to be sabotaging myself.

So I've been contemplating a schedule more like this:

M- Strength Training (Upper)/ Run
T- Class
W- Run
TR- Strength Training (Upper)/ Class
F- Run
St- Strength Training (Lower)
Sn- Rest

I've been doing the Upper/Lower split for two weeks now and I definitely find it less tiring. I also dropped a lower workout, my thought process was it's not my focus and I'm really only concerned with not losing muscle mass/strength. I don't need gains right now (once the half marathon is over the plan is to dial back my mileage and go back to a 4 day upper/lower/upper/lower split).

Does this seem reasonable?/ Still crazy? Is there some way to do this better? Other suggestions? thoughts?

I can't move the class or Monday strength training but everything else is flexible.