I am not a pro at this by any means but, I can tell you what I see. In the jogging video I see the rider working the reins to get his head down. This should not happen. Head down should be a leg cue. Squeeze and his head should drop. You can teach this fairly easily by having him stand and squeezing your legs and reins until he lowers his head. Do this every time you ride and slowly decrease the amount of rein you use until it is all leg. Then do the same at each gait.
In the loping video he is very heavy in the front end, which you already know. To fix that you need to get him off the bit. You can start by loping a few strides(no more than 5) then stop, back and lope off again. Repeat this until he gets lighter in the front and then let him lope like normal. If he starts getting heavy again, do it again. You can do the same thing at the jog to smooth out his stride a bit. And it should also help with the head bob because that is caused by him pulling himself forward with his front end.
These things are easy enough for me to teach and I'm not a professional trainer by any means. You have a very nice horse! Good luck!
Thank you. This is what I wanted to hear and thank you for the advice! Normally when I ride him, I give him his rein and he doesn't give me any problems dropping his head and he is very sensitive to his leg pressures (no spur wise). He really does feel like a rocking chair when I ride him in the lope as I like to sit back a bit and I can feel the changes. I suppose it could be the rider at the time? Anyways, thank you. He's very special. :)
Proud Partner Owner of Me Too Radical, Top 10 PQHA Quality Improvement Program Futurity. Sire of AQHA, NSBA, and NRHA champions. Sweet, gentle, excellent mover, excellent temperment, and so much more. Standing in Indiana.