The lye is very water-soluble, and the DPT base is not as far as I can discern, so the froth should only have had as much as the total volume of water divided by 200mg times the amount of water in the froth. A milligram or two at most? The boiling point is 1300+ degrees like you said, and DPT's is <100, so while you might end up inhaling a few nanograms or micrograms of NaOH, it should go unnoticed.
If you can calculate the molecular mass properly, and you have a known 60mg or so of unreacted NaOH, the correct molar mass of acetic acid should form sodium acetate and DPT freebase along with NaCl left over from the initial NaOH + DPT HCl reaction. You'd have to chop the frothy remains up good and mix it into the acetic acid to make sure the various compounds had a chance to reach an equilibrium. The acetic acid and NaOH are far more attracted to each other than the DPT and acetic acid. Let it settle and maybe freeze it, pull the DPT out, and what you have now should be as close to pure DPT as you'll get. I don't know enough about the properties of DPT to know if it's possible to cleanly get all the DPT base out of the water solution, but it seems to make sense to me.