How can I prevent my AC condensate pipe from making my soil soggy?
Connecting condensate and sump pumps to sewers is rarely legal these days in most places, so concentrating on a dry well approach is probably best unless you have dedicated storm sewers you can legally connect to. 

One "crude but functional" test of "size of hole" is to dig it (and not fill it in, though depending on accessibility to the public you may need a temporary fence to keep children and people who should know better from falling into it) and either add water or let the condensate drip, and see how fast it goes away. The point of a dry well is to provide storage, and a larger surface area to drain away into. If you get lucky (don't count on it) you might get through the clay layer and have much better drainage - but in any case you will have a larger area to absorb water. Most dry well systems are amenable to put one in, if insufficient, add another, (connected by pipes underground) until you get sufficient percolation into the subsoil.