I was stuck aqua jogging my sophmore year, and with 4-5 hours of that each week and three solid lifting days, I ran 3:53 (which was at the time like a 4 second PR) off of 10ish running miles a week. I normally lift two sessions a week, with a push day and a pull day, probably 4 exercises each session, done at 4-6 reps each for 2-3 sets.
Your normal run pace and your tempo pace are a bit faster than mine, with your mileage being a bit lower. This is probably due to the difference in our running styles, and I'm certainly not going to over-analyze it. Consistency is really the key to improvement, so I'm sure you'll do fine this season.
But seriously, your legs get sore after lifting because you aren't used to it. The more you do it, the less Delayed Onset Muscle Soreness you'll have after. In the same way that you now run so much that you aren't sore from normal efforts.
Sample routine:
Warm-up: 5-10 minutes
Cleans: 2 sets of 4 heavy, around 4 or 5RM, scaling down for safety. (Reset position and grip inbetween lifts if necessary. Probably wouldn't do these if they hadn't been taught to me)
Box Jumps: 2 sets of 4 jumps, challenging height or 2 sets of 10 jumps medium height
Squat or Deadlift: 2 or 3 sets of 4-6RM-ish (add variation with front squats or the trap/hex bar for deadlifts or RDLs when you feel like it)
Accessory lifts: Pretty much do what makes you happy
There's some good literature on why lifting has translation into more efficient aerobic muscle work, and a little bit of power never hurt anyone trying to kick to the finish. Keep your mileage up and your calories at a reasonable level and you won't gain muscle mass on a program in this range.