Reynolds number surely has an effect, but that is dealt with for instance by the LE radius. I think most of the problems with scale models come from their excessive weight. For instance, you need the bigger tail to have enough damping with the big moments of inertia. Try alasdair's spreadsheet to calculate a scale-like weight, probably you would be surprised. At least I had this surprise when I tried a few models just in the simulator. They were beasts at their real weights but became kittens at a scale-like (far lower) weight (mass).
As to power-to-weight ratio, more drag at model-size Reynolds numbers is probably the least of the problems. Actually, the more wing loading the more P/W ratio is needed. Still most models today are over-powered, what substantially contributes to excessive weight. Just see what alasdair wrote in the other thread.
And retaining the same flying characteristics as the full-size original has is just about impossible on a model, again due to its weight. What alasdair's spreadsheet calculates is a reasonable compromise between scale-like speed and scale-like movements. The resulting model weight is so low that it's rarely seen on actual models, meaning many scale models can't fly scale-like anyway.
Years ago we had a
thread here at RCU about a scale-like flying DC-3 model. It turned out that about the only thing that made the model flyable at low speed were flaps. I would recommend flaps to the OP here as well. (Split flaps are simple.) And flaps as well as washout were effective only if wing loading was reasonably low in the experiments back then.
Thin airfoils were not a problem, indeed they are more efficient than thick ones at low Re numbers. The thicker ones with the round leading edge begin to stall at quite low AoA but they don't lose lift. Their drag increases to very high values, though. That could be accepted at the wing root to have a lighter structure, but tapering to thinner airfoil with less incidence (washout) to the tip is a good compromise.
By the way, there are even reliable wind tunnel data at model Re numbers for a few airfoils, for instance NACA 2415 (even with flaps).