HIIT Programming - Routine Check

I lift 4 days a week on lunch hour, loosely following the original 5/3/1 format. I’m able to use a gym at work for 3 of the days, but have to commute to a local commercial gym to squat (no rack at work). I warm-up thoroughly using self-myofascial release with a tennis ball and foam roller, and some mobility drills - this takes about 15 minutes (and I really feel I need it - I’ve been injury free basically for a very long time and I credit this work largely for it).

I want to incorporate more athletic movements into my routine, but I do not want strength gains to suffer. I don’t want to get big and slow - I’d like to retain at least some of my athleticism into my later years (I’m 43). My midsection is a bit blocky looking as well - not terribly fat, but big, and I’m thinking that higher rep ab work (higher reps than I have been doing) along with some more athletic movements might help this (diet, of course, being a factor also).

Being a fan of the 5/3/1 system and looking over Wendler’s latest iteration which incorporates some throws and jumps, I’d like to incorporate these along with some HIIT, all being pressed for time at lunch hour. It is a lot to fit in!

I wanted to get the opinions of some of you seasoned lifters. I follow some of your logs and really think that you all have a lot of knowledge to offer an older guy like me with a busy schedule.

So here goes, as far as what I am planning to do:

Upper body warm-up (as described above)
Overhead medicine ball throw 1 x 10
Press 5/3/1
Pull-up/Chin-up BW 6 x AMRAP (between press sets)
Dip BW 3 x 15
Dumbbell Lateral Raise 3 x 15 (between dip sets)

Lower body warm-up
Standing long jump 3 x 5
Deadlift 5/3/1
T-bar swings 3 x 15 (between deadlift warm-up sets)
Side Plank 3 x 1 minute per side
HIIT 10 minutes (most likely sprints outside)

Wednesday Off

Upper body warm-up
Medicine ball slam 1 x 15
Paused Bench Press 5/3/1
Face Pull 3 x 15 (between bench press warm-up sets)
Cable Row 3 x 15 (between bench press work sets)
Low Incline Dumbbell Flies 3 x 15
Barbell Curl 3 x 10

Friday (commute to commercial gym, so time crunch)
Lower body warm-up
Squat 5/3/1
Box Jump 3 x 5 (between squat warm-up sets)
Ab Raise 3 x 15
HIIT 10 minutes (most likely manual treadmill sprints where the power is off and your leg drive makes it go)

Weighted vest 2 mile walk

Sunday Off

Will this routine work? Is this enough lower body work to maintain/gain strength?