I wouldn’t throw money at the Recons, and the forks from Flatout will be second hand. Many many many people ride poorly set up forks, and the range of adjustment on cheaper forks may not cover your needs.
What is the problem with your forks? Are they blowing through the travel, or is it more the rebound getting overwhelmed? O wouldn’t worry about the Rockshox recommended pressures. These are generally nonsense in my experience. What feels right and works is best.
Maybe a service with fresh oils will rejuvenate them? If they are motion control, stick with the recommended oil levels in the damping leg, but think about a heavier oil – maybe 7.5wt?
A small (and I mean small) amount of oil in the air side will help make the spring more progressive if your sag is OK but you are bottoming out. Keep the lowers well lubed too.
Recons are simple forks to work on and you can experiment with weights and levels. I wouldn’t bother with a pro-tune, and I’d save your bonus towards a mid to high range fork from someone who can set it up/tune it to your needs.