First things first: you run pretty well! Surprisingly well, in fact!! With that stated, there are certainly areas you can and should address. While there are things we cannot help (namely, your knees), there is much still that can be done: eliminate the right lean, increase left hip extension, increase lateral strength.
Given your background, I’m sure it’s redundant to write this, but I’ll do so nonetheless. Think of the pelvis as a pulley…or better yet, as an orb (basketball, soccer ball, whatever your choice). Now picture that ball floating on the surface of a calm pool. If I push down on the right side of the ball, the left side rotates up. If I pull up on the back side, the front rotates down. Muscle imbalances around the pelvis have the same effect. Either tightness or weakness can force/allow the pelvis to shift right, left, forward, back, rotate right, left, forward or back. Or any combo of the aforementioned.
Based on what I see on video, these imbalances are definitely causing the asymmetry in your gait and most likely are causing the right foot 5th styloid pain (or at least continuing the pain after the narrow shoes let the genie out of the bottle).
To help with your gait, we need to address the muscles that rotate about the z-axis (the torso and hip lateral flexors), about the y-axis (hip rotators, int and ext obliques, lower traps) and for the most part ignore the rotators about the x-axis (quads are a no-no, but hopefully glute max and psoas can be addressed).
First things first, here are your run videos:
***NOTE: I intended to mesh the anterior and posterior on one screen, but the pausing did not sync. The best way to view these is to open two windows and pause manually to keep them in sync (sorry it turned out this way…I only discovered my error once I had completed and to fix it would mean keeping you waiting another day).
***NOTE: Upon reviewing this video, I see I erred in marking the hip extension measurement. The left side of the screen (measuring the right hip) is correct at 174 degrees. The right side of the screen (measuring the left hip) is incorrect (I inverted the angle). Instead of 179 degrees, it should read 181 degrees. In other words, your left hip actually extends past neutral, while your right hip does not.
QL STRETCH (to address high right hip, perform 20-30 seconds post work out and as needed)
ITB STRETCH (to address high right hip, perform 20-30 seconds post work out and as needed)
QUADRIPED (to address lateral strength, perform 10-20 reps, 2-4 sets daily or as tolerated)
SIDE BRIDGE (to address lateral strength, peform 10-20 reps, 2-4 sets daily or as tolerated)
GLUTE AND PIRIFORMIS STRETCH (to address hip extension, peform 20-30 seconds post workout and as needed)
STANDING PSOAS STRETCH (to address hip extension, peform 20-30 seconds post workout and as needed)
TURKISH GET UP (a fantastic and difficult exercise to address rotational and extension strength, perform 10-15, 1-2 reps per side with very VERY light weight…and study the video for proper form!)
MYRTL ROUTINE (a GREAT all around hip strengthener and mobilizer routine, BUTTTTTTT the athlete in this video performs these exercises WAAAAAAAAAAY to fast, perform up to 10 reps of each in a slow and controlled manner; eliminate any segment that causes pain)
LEG CROSS OVER STRETCH (to address torso rotation, perform 20-30 seconds post workout and as needed)