Are you saying that the presence of CaCO3 is making the CaSO4·2H2O dissolve faster than it usually would
Not presence of CaCO
3 but presence of carbonates in general - wood ash contains a lot potassium and sodium, I expect sodium and potassium carbonates.
As though the CO32- ions are actively replacing the SO42- ions in the solid gypsum crystals?
Yes, that's the problem I suspect.
And if this is the cause, do you expect that first reacting the CaCO3 (in the ash) with an acid would be beneficial? Or could I 'rinse' it out with excess water and then filter to be left with just the non-reactive solid particles in the ash?
As explained above not CaCO
3, but carbonates in general, but yes, treating them with acid will remove CO
2. To keep things simple I would use sulfuric acid, that's a common ion with the CaSO
4, so the interference would be as low as possible. Trick is, after treating with the acid ash will be no longer the same ash you started with, so its properties can be completely different. No idea what it will mean for your application.