Yeaahh....That's the problem right there. That's not doing shit for your glutes or your abs. Especially because it's too damn easy to hang on the anterior ligaments of the hip in the plank in order to get more time out of the plank and thus the illusion of "progress".
Try 6-9 sets of ab work every time you're in the gym. Actual ab work, don't be feeling shit in your hip flexors. Keep your lower back from sagging down, that puts all the strain on the back and the anterior structure of the hip rather than the abs. And stretch your hip flexors both in warm-up and before your ab work later--tight hip flexors "stick" your hips in a position where the lower back gets taxed much more (anterior pelvic tilt).
Roman chair leg raises
ab walk-outs (similar to roll-outs but using your hands to walk out)
stir the pot
plank with your hands on a medicine ball
reverse crunches (push-up position, shins on a medicine ball, pull your knees towards your torso)
Shit goes on and on, that's not even counting oblique exercises--which probably don't need to be focused on right now as you're so weak all around in the core.
Work them seriously. Pick 2-3 exercises and do them each for 3 sets of 8-12 reps--like a circuit/superset-- with as little rest between as possible at the end of your workouts. Exception is the planks, which you should be squeezing the life out of not just hanging out. ALSO pick 1 easy exercise and do 3 sets during warm-up to get them activated.
Glutes, again not getting enough work. Your plan might work for people who can already activate them and/or are naturally glute dominant but not for you or most people.
bodyweight glute bridges (again, no arching of your low back on any of these, keep your abs tight)
single leg glute bridges
dumbbell or barbell hip thrusts
sideways walks with a band (also known as X walks or Monster walks)
and a bunch of other exercises are all good. Do a bodyweight exercise in your warm-up right after stretching your hip flexors and the ab exercise. Every day you're in the gym no matter what. Then as a "pre-fatigue" exercise before both squats and deadlifts--but especially deadlifts--do a dumbbell loaded glute bridge. Stop before failure, do it as a superset--deadlifts and squats are the 2nd exercise of the pair. Again, you're not allowed to arch the low back, you have to squeeze the shit out of your abs while you do these exercises.
Standard mobility drills are pretty good yes...but it depends on what your definition of standard is lol. My definition and yours may be very different.
Honestly, I don't think you need to lay off the squats and deadlifts. I've had damn near crippling aches in my mid back from maxing on good mornings, I still managed to train legs the next week. Give it a week off the squats and deads, and substitute a pair: 1 ab exercise and 1 glute exercise from above, done superset fashion.
Strangely enough, stretching your back MAY be helpful in getting your aches to go away. If you are suffering from back extension based pain, then actually some flexion may help alleviate it by bringing you back to "normal", but this should be seen as situation specific and never a standard procedure, like I said above don't stretch the back when lifting. Play it by ear, but always away from your workout. If you feel less pain, keep it up for a couple days, if not then stop. There's no sense in stretching it if it is not making you better. In that case you may gradually be making things worse. Too long to type that one out, but that's the short of it.
Think of it as an iron rod--the strongest position is straight. If the rod is flexed forward, then to bring it back to "normal" or straight, one should extend the rod more. If the rod is extended and bent backwards, then one may be able to flex it forward more to bring it to neutral. Flexed forward would be like a desk jockey always slouching at a computer. Extended back would be more like your present situation (or google 'anterior pelvic tilt' for a visual illustration). Now that's not a really thorough treatment of the subject and therefore the analogy "rule" isn't a hard rule but more of a general guideline. In general stretching the low back is something to be avoided for the reasons I mentioned above. It is still my least favorite method whatsoever of trying to correct a postural problem because it builds in its own weaknesses.
Oh, and 3-6 months off squatting and deadlifting is fucking bullshit advice. Did you break your spine or your legs? No? Well shit, probably ought to fucking keep it up. But...you also had probably better learn to do it right lol.