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sounds like you need stronger quads as well as stronger glute/hams etc.. stronger everything.. if you train people in person or pay attention to people's logs on various forums, alot of people with knee pain are just too weak in the lower body, they usually have underdeveloped vmo's or vmo's that don't even fire properly in relation to the VL.. you'll want to perform TKE's (terminal knee extensions) & squat, just work your way down slowly if that's your goal, but for now stay slightly above parallel and progress very slowly with some weight on your back or in your hands... go very light on tke's, it's a high rep exercises 20+ reps focusing on really contracting the vmo.

the quads are more important than the hamstrings for knee stability imo, especially for jumpers.. people with weak vmo's will have all types of patella/knee issues, people with weak hamstrings well that's a toss up - some have issues some don't, but EVERYONE who has weak vmo's has knee problems because the patella tracks improperly during knee extension.. i'm not a doctor/pt, and i havn't seen you in person so i don't know if this is your case, all i'm saying is, in your quest to become glute dominant, do not neglect the quads.

add in 'half squat' (slightly above parallel), improve depth if you want but make sure improving depth doesn't freak out your knees, do not try to sit WAAAAY BACK, that'll probably aggravate them even more, just go right down basically, get more quad involvement.

on the back extensions make sure you're using the glutes to extend.. i'll have my back extension soon and i'll video how i do them, should help.

i like walking lunges for distance, if you can't do that then ya reverse lunges are good, but walking lunges are #1 imo.

How is working on ankle mobility, hip mobility and glute strength going to help your knee condition? There might be a correlation between "quad dominance" and knee problems, but that does not mean that getting rid of "quad dominance" helps an already existent patellar tendinosis. It also does not mean that "quad dominance" is the cause of knee problems. If you thought that was the case you should read up on the difference between correlation and causation.

You are on a bad track to solving your knee issues. You have to figure out what actually caused those problems in the first place, like jumping on concrete everyday for hours (that's an example). Having "strong" quads in relation to your glutes is unlikely to be the cause of this "patellar tendinosis", as unlikely as ankle or hip mobility. You also need to understand what is preserving your knee problems right now and what prevents your body from healing. If squats aggrevate your knee pain you should not squat - at least not with the technique you are using at that point. If there are exercises that you can do pain free, do them. But let that knee heal up.

Don't forget hip flexor stretching.

Bulgarian Split Squat targets hamstring and glutes like hell!! I love BSS! try it and you'll not regret it.

Do I understand correctly that you are doing bodyweight squats - meaning squats without a weight on your back?

Where do you think does your patellar tendinosis come from? If you think it's the squats just stop doing them and see if that helps the condition. It's not that squatting with your bodyweight will accomplish much in the first place.

Also I don't see how you doing "core" strengthening exercises is related to that patellar tendinosis. Maybe you want to help me out with that.

How does overactivity of one muscle compared to another (if such a concept is even worth thinking about) explain the development of a chronic tendon injury? Where is the link that I fail to see here? And how do you diagnose over- and underactivity anyways?