My solver's found about a thousand so far, here's a good one: "abyes choup donut dingo" (note that there are a number of 'fake' words allowed for guesses).
abyes GXXXX
choup XXXXX
donut XXYXX
dingo XYYYX
matches both
aging, again
so this solution doesn't actually partition the solution space the way you want it to.
My solution is static and doesn't take any clues into account, so what you're saying just doesn't feel very relevant. The only "solution in general" to an arbitrary adversary, if you're not allowed to look at the clues it gives, is just to guess every single target word, which isn't very interesting.
Now, you could easily argue that the greedy strategy used by the site is suboptimal, and I'd agree, but AFAIK nobody's put up a site with a better one yet.
choup xxyxx
donut gygxx
dingo ggggg
:D
I used a much larger dictionary for allowed guesses than for the actual words that get chosen.