What would you need a custom factory for? This is perfectly acheivable with MC's default factories - see here and here.
@AlmightyElement
Either use OreDictonary if you want all logs to be accepted from all mods(that register their logs to the dictionary that is) or specify two items in your ingredient(example) because the game has 2 separate items that represent itemblocks for logs for whatever reason with the data set to the wildcard value.
Edit: if you want a separate result per log then you will need one recipe per log, with the data property being incremented by one for each variant. And yes 2 of your recipes will have a different item name than the other 4(for vanilla)
Line 89 in the file MoCEntityTameableAquatic.java is trying to cast an integer to a boolean which it cannot do, probably because the integer is neither 1 nor 0. It's a bug and needs to be fixed by the developer.
You can also override the recipes with dummy recipes that do nothing, as I do here. The DummyRecipe class is here.
This prevents the advancement errors, but instead spams the log with "Dangerous alternative prefix" warnings because you need to set the registry names of the dummy recipes to the registry names of the vanilla recipes they override. As LexManos said here, there's currently no way to avoid this.