Getting a big lift to go up at your level of experience is about 1) fixing weaknesses and 2) improving technical efficiency
The one life that would really help you is the Frankenstein squat from the bottom (starting the bar from pins):
(as a bonus you get to see my singing skills)
This movement is awesome to strengthen the torso and upper back rigidity in the front squat.
I would also recommend the fixed weight progression for your front squat:
Using about 75-80% of your max... keep the same weight every week.
WEEK 1: 4 x 3-5 reps, regular reps
WEEK 2: 4 x 3-5 reps with a 2 sec pause during the eccentric (lowering) at the mid-range
WEEK 3: 4 x 3-5 reps with a 2 sec pause during the CONCENTRIC (lifting) at the mid-range
WEEK 4: 4 x 3-5 repos with a 2 sec pause during BOTH the concentric and eccentric
After 4 weeks you would add 5kg and start the cycle over
It is important to not allow yourself to cheat by bending forward, only allow technically solid rep, even if that means starting a bit lighter.
I would do the Frankenstein squats on one day and the fixed weight progression on front squats the other day.. On the Frankenstein I'd do something like 5 sets of 3, resetting on every rep. Start from your bottom position.