Strength / Weight Training

If you don't want to put on size steer away from higher hypertrophy reps and just focus on strength. 5x3 or 5x5 will do the job. It'll make you stronger, which is your goal and you're unlikely to put on significant mass unless you up you're eating too. Do a 8-12 week period and see how you feel at the end of it?

It's difficult to build any meaningful run endurance with weight/strength training, because even a 5x20 is only 100 reps and a weight that you could lift for that lot would be wasting a lot of potential strength gains for the time your investing. How many steps/reps does your typical run have!

When I started lifting, as a reforming run addict, my coach suggested just doing squat, press and Deadlift which would make the most of the single session per week that I was able to commit to.

Warmup with empty bar 3x5
Build up weight over 3 to 4 sets, whilst dropping reps to 1.
Working weight 3x5

Deadlift warmup. Bar with 5 or 10kg bumper plates 3x5.
Build up
Working weight 1x5

Obviously depends how you progress, but add 2.5kg for squat. 1kg press and 5kg for Deadlift each session and you will quickly find it hard. When required, increase your rest times through 4, 5 up to 6min and once the big weight increases are too much, reduce the weight increase to 1.25, 0.5 and 2kg.

My suspicion is that won’t work. I think you are trying to improve core strength - squatting will do that amongst other compound lifts.
Heavier weight will require stronger core.
I think I’m starting to get boring by mentioning Stronglifts yet again!