i think that based on what you’ve said, that you have some left/right side imbalances that have been around for a long time and they are rearing their ugly heads as you load your system.

i also think that given the tightness in the QLs and low back, that you are:

1. not engaging the glutes enough

2. have not good enough bracing via intra abdominal pressure – you’re depending on the muscles around the core to do the bracing and not supporting it via IAP.

i cannot tell if this is a debilitating problem or not, but if it really bugs you, you should work on movement pattern first and proper muscle activation, then start to load it.  if the loads you are using now causing enough problems, then i would lower the loads until these problems subside somewhat. or remove the loads all together and only focus on bodyweight and the movements with a light bar.

i know you are a veteran of MWOD and these forums so keep working on the mobility up and down the chain. however, there are not so many videos on motor control. for that you may want to find a good strength coach to help you figure out your form properly.  I do not know if Diane Fu is available but she would be great.

As for the imbalances, it may mean some supplemental exercises to help get more balanced.  Someone who is trained in FMS level 2 would be helpful here.  I am personally a fan of those certified with SFG and working with kettlebells in a targeted way would help a lot.

Proper abdominal breathing would be crucial in generating IAP for a properly braced torso which allows breathing.  If you are chest breather, you should look at working on abdominal breathing and using that abdomen breathing to generate IAP. Teaching that on this forum is probably too hard though.