The front squat is a good choice since your weakness appears to be the quads. I would do them is a 2 sec pause in the bottom position focusing on maintaining perfect body position not on the load.... so something like 5 sets of 3 reps NOT using the double progression would be best. The double progression is a fine progression model but I don't like it on front squat since it will often lead to bad form just to "get the reps" because you HAVE to improve. I would just do 5 challenging sets of 3, leaving 1 or 2 reps in the tank, focusing on perfect form. Add weight when it feels too easy. I know it's not precise, but sometimes you can't go with rigid progression models.
The lunges are a good idea (I prefer walking lunges), make sure to take fairly short steps to focus more on the quads... lunges are quite likely the WORST exercise to use the double progression model on, don't use that... do 3-4 demanding sets but never breaking form, add weight only when it feels too easy.
I don't like hanging leg raises for abs, it makes great pictures but it is not a great movement. Especially if you are weak out of the hole in your squat, it will tighten up your hip flexor which will make it hard to be in an optimal positon in the bottom position of the squat