Following the "make your hard days hard" philosophy, I am thinking of doing speed work on my strength days (run in the mornings, lift in the evenings).
This is what I do. When you get to the lower body strength, just keep in mind that you'll be starting with tired legs if you have speedwork in the morning. You might not be able to do as much as you would going into it fresh.
I'm really new to strength training and my first leg day wiped me out.
That's normal! It will get better. Just make sure you're building up slowly - if you're ever so sore you can barely walk, that means you did too much and you need to dial it back.
I'm not sure where to put my long run. Mondays or Sundays? I've typically done my long run on Saturdays, then rest on Sundays, but I don't know if I'm going to be able to do that if leg day is Fridays.
Mon - long run? - Kung Fu
Tues - rest
Wed - speed work/upper body day
Thurs - Kung Fu
Fri - speed work/ leg day
Sat - recovery run? or long run?
Sun - or long run here? or rest?
I would say you're probably better off not doing a long run the day after speedwork/lower body strength. I would think either Sunday or Monday would be okay, but see how your runs feel once you start getting used to those strength days and that will give you a better idea of what works for you.
Example of what I'm doing currently:
Mon - easy run/upper body strength
Tues - easy run/lower body strength + HIIT
Wed - easy run/core
Thurs - rest
Fri - speedwork/total body strength
Sat - easy run/core
Sun - long run/yoga
I consider Tuesday, Friday, and Sunday to be my hard days. I basically replaced a running workout with harder strength/HIIT, keeping in mind that supplemental training is also part of the 80/20 balance you're aiming for overall. I wouldn't necessarily move upper body strength days automatically into the "hard" category, but I've also been doing strength training for a long time, and I'm generally not lifting so heavy that I'm sore the next day.
When I had karate classes, those were more likely to make me sore, so I would have tried to line up harder runs with karate rather than strength and probably kept the strength a little lighter. I think it's really particular to your own experience - when do you feel the most tired the next day?