Ok, as a caveat, I am currently a physio student, not qualified.

With cycling, there is a tendency for people to let their knees come across the front of them so that they are not pedalling in a biomechanically sound position. I see this on the club rides that I do week in week out. I would actually look at the strength of your gluteus medialis alongside the pelvic tilt issue. If psoas was going to refer pain, it wouldn't be referring it to the inside of the leg, it would refer it down the front (femoral nerve route). The femoral nerve passes through this muscle, and therefore if this was going to be problematic I would expect a different pattern of pain than to the medial knee.

With the right leg being shorter than the left, could it be that the adductors and sartorius are being chronically shortened even when off the bike? Do you get pain relief when performing a stretch for the groin? Related to this, I would be suspecting an involvement of the piriformis muscle due to sciatica type symptoms of burning pain down both legs when performing a stretch - could either have neurological shortening of the sciatic nerve which when put under a stretch gives symptoms (slump test) or the movement is causing the potentially inflamed and overworked piriformis muscle to compress the sciatic nerve. Cycling frequently with an adducted leg would stress and inflame piriformis?

So, what would I do? I would want to strength test your ABductors (glute med particularly) and work on building strength there. I would also want you stretching the groin area as much as possible, alongside psoas. The test you describe from your last post sounds like the Thomas test, and it sounds like you were definitely positive on the right side. I would also want to do some manual therapy on what I suspect will be a very tight and angry piriformis that is giving you burning pain from time to time. Have a look at this:

YouTube - ‪DeFrancosTraining.com - Piriformis myofascial release‬‏

I would advise a medicine ball would be best to start on as a cricket ball (or whatever he is using) may well be too much. For glute medius strengthening exercises (very important to you as a cyclist) I would perform:

1) Hip sinks - standing sideways on a stair keep your supporting leg straight. Then let your hips sink down on the side of the leg that is off the ground (without bending your supporting leg's knee) and concentrate on bringing your hips level again by squeezing in from the side of the buttocks. Imagine you are trying to hitch your hip up as high as you can before letting it drop back down again in a controlled manner.

2) Sideways leg kicks - as you are looking for functional stability in cycling. Kneel down and then support one side by putting your hand on a raised surface (about a foot off the ground). Straighten the top leg and then lift this off the ground. You should know be on one knee, leaning on a surface with one hand and with the top leg straightened and just off the ground. As you bring the leg back breath in and focus on not letting your hips fall forwards (what yours do currently) by tucking your stomach underneath you. Then, bring the top leg slowly forward breathing out before returning to the middle. Do this very slowly - you should notice that both sides of your hips are really working hard, especially as I suspect you are very weak there.

3) Hip ABduction - With a theraband or stretch chord, wrap around both ankles. Stand tall and aligned and then push one leg out as far as you can before slowly returning to the middle. I can't find anything on youtube, but basically this YouTube - ‪Joyband but stood up and with the band around your ankles not thighs.

With all these, perform a maximum of 10 very slow controlled repetitions, 3 times every other day. If you can't get to 10, stop when you fatigue. You could try every day if you don't feel tired, or simply use a heavier resistance on the band. I hope the explanations are ok - it's really hard to find any videos of these exercises on the net, and describing them is tough.