Wick is right that I am a fan of Citristrip but I also recommend one chemical paste stripper, Peel Away. It is good for that project with 15 coats of paint but overkill, I think, for yours. Some other chemical strippers are methyl chloride based and I just will not use them. I used a lot of methyl chloride over the years and am now concerned about what it will do. I don't have the same concern about the NMP based strippers.
Wick, if I ever told anybody to use a stripper and didn't tell them to wear gloves and eye protection, I screwed up. But it's amazing how much you change as you get older and, hopefully, wiser.
Dodgeman, I think that a stripper like Citristrip would be a good choice for you. You don't have a lot of finish to get off. I will say that you can trade speed for safety in your choice of strippers. Glob Citristrip on with a cheap, wood handled, natural bristled brush and try not to overbrush it to get it smooth. Come back in an hour or 2 and see if the paint and finish appears to have released. If it has not released, go back to watching the ballgame on TV for another hour. If it has, remove the goo with a putty knife or whatever other tools that you can think of that seem to work for getting in the small corners. When you have all the goo off, wash it down with Citristrip Paint Remover Wash or mineral spirits.
Wick, I used to use steel wool but I got a couple of finish jobs that appeared to have redish brown measles that I attributed to the small pieces of steel wool getting down in the wood and later rusting. These were not a big deal but I quit using steel wool and the problem went away. This was worse on oak and ash so it may not be a problem on birch ply.