Any way you can rig up a scheme to have a plain water rinse for each frame (inside and out!) as you cycle each through your acid bath? That'd go along way to eliminating much of the carried-out acid solution. Or even prepping a bicarbonate solution (cheaper than oxalic acid) to do a cursory internal neutralization before setting each frame aside for a few days?

After all these baths it's A Good Idea I think to give each frame a decent rinse with plain water before proceeding with the next steps in your plan of action, then thorough dry-out. Gets rid of any remaining contaminants, leaves a clean surface for whatever you might have in mind for overcoating (lacquer inside, or oiling) before re-assembly.