Regarding the "end goal" - I understand you pretty well. I have similar struggle! What I think works for me is the "constant small iterations" approach. I try various things and go on with those that feel right. For example I found it tiring to play the levels all way long, so I decided to introduce cards selection - like your perks. It was not enough, so I decided to go further and introduced the store. It's pretty basic right now, but I've already got some meaningful feedback around it. I still might get rid of it, but at least I validated the idea.
I think your current goal - using X out of Y blocks works well. Weaker players are able to progress, while better players have the challenge and risk vs reward feature - they may decide to skip some block which could finish level with 95% in order to get two more blocks to get the 100% - at least that's how I perceive it.
I feel like you rather have the same issue like me - you have to add some feature that allows players to rest from filling blocks for a while. I think Balatro's shop is a game changer and something you should try. You could also try collections like in picross games. If you want go mobile, you could try daily challenge, etc.
Just pick up one that fits best for you. I'll certainly try it :)