Reddit mentions of AMTECO DIVISION OF GEMINI INDUSTRIE TWP-1501-1 Gallon Cedartone VOC Stain

I would powerwash it and let dry for a week or so, then do one of two things:

1. find the best quality paint that will stick to the existing paint and to the exposed wood. Repaint every 4 to 6 years. I don't know anything about deck paint, but research and find best quality possible.
   
   
2. more work in short term, but better option - get a powerful sander that you can attach a shop vac to, wear ear protection, and sand all that paint off. i would use rough 60 grit and maybe a pass with 100, but not worry about getting it too smooth. then seal it with a high quality sealer/stain, which will need to be reapplied every 5 to 8 years. I used a product called TWP based on a recommendation from guys at the best lumberyard around. They said their contractors find it lasts almost twice as long as products like Thompsons. It was very easy to apply, just soaks right into the wood. Contains a fungicide so keep it off your skin while applying. 2nd coat a few hours later then about 5 days to fully dry/cure. Note that the low VOC version works great and that the clear version does not have UV blockers which allows the wood to turn gray. It goes on so easily that I can't imagine painting a deck would be worth it.
   
   You possibly could flip those deck boards and have a clean, unpainted surface. Worth checking out. May look like new under there.