Also dont get obsessed about parallel. Only go as low as you can properly. Over time you should be able to get deeper and deeper.
Alex, I have never understood why you would recommend that to a guy, especially a beginner, over the internet. I can to a degree understand why in group coaching situations with team sport athletes you might not have the time to coach a full squat to everyone. But this person is trying to learn full squats, because they are a better exercise for a beginner, and needs to be introduced to correct form as long as the weights are light. I doubt that doing it wrong now will make it easier to do it correct later. In the process of doing squats high nothing is learned that helps doing squats low later, since in most cases technical problems are the reason for the inability of reaching good depth with reasonable form.
If he is spilling into his low back, quads , and hamstrings then he is not squatting correctly (if performance is your goal, squatting for OLY or PL is different). He needs to be getting to his glutes. Depth has nothing to do with this, proper movement does. So why not move properly. The OP said he no longer gets his glutes going in squats and loads his erector spinae and hams during DL's, thus It seems safe to conclude he is losing position or form.
I recently saw a few McGill presentations in person and he echoed the same points. Going to parallel for parallel's sake in the face of bad technique (not getting to the glutes) will lead to injury. He also asked people "Why do you need to get to parallel?" Everyone said the sme thing "P-chain..." His response was that if that is the reasn you have never seen a properly conducted EMG study or have a very poor understanding of functional anatomy. I sat there and wondered how many heads his presentation was fling over at that moment.
So in summary only do what you can do with perfect form and over time proper strength development may open up new ROM's