Yes that is a progression and yes keep doing them in the workout. For skill work continue to get up against the wall and do a couple HSPU. You will get there. We all have been there before.

Protein is needed to both build and repair muscle- even those who eat well- often do not get enough lean protein.

Having small increments for SP is good too, for instance I can increase 1/2 or 1 pound a week on SP by just adding that to my sets, (obviously this will top out at some point. )We have 1/8, 1/4, 1/2 1nd 1 lb plates- this has been very helpful.
Also the HR set after a strength set is helpful. Use about 80-85 of max and do 1 rep every 30 seconds, or go for constant motion for max reps.