Troy, I personally came across the same conundrum with some of my athletes. Whether to take them off training the planche because their L-sit was poor. I think the ones that had this problem may have become unhappy or felt slighted when others were working on the planche and they were not allowed to.
We also had the luxury of 3 hours workouts and then the L-sit and presses were done early on within the first hour and then we would hit the planche and levers towards the end of workouts besides having a snack break halfway through workout. We also would do planche and lever work right after the basic L-sits and presses but would do pullup, pushups, leg lifts, etc toward the end of workout.
Until your L-sit catches up, your planche and other levers may stall out. For my athletes I let continue to work on the planche and levers, but they would also have to split up that time with perhaps extra L-time in hold or support. I let them continue to work those planches and levers, but I knew they weren't really going to get anywhere with them beyond until they caught up. However, they found them fun, so I relented. Besides, they wanted to be like the stronger guys.
I know for myself, I noticed a decrease in the performance of some of the statics and ROM exercises after going through the whole L-sit, straddle-L, planks and basic warmup supports and hangs. You have to do x amount very carefully or it would just overtax me. Sometimes this was due to the fact I would suggest do a 1-1.5 L-sit, my max and move on whereas other times I would split it up or do a total volume of 3m of L-sits, which I built to eventually.
Just keep that in mind with your warmup sets, because it frustrated me a bit.