The type of fingering I showed you, using the 1-3 rather than 1-2 and relying more on 3, 4 and 5 than other people might, will work, I think, for this Invention.
It won't work for everything, though, so there is another technique you need to consider. It is essentially the same as is used in more advanced pieces, such as Chopin 10/1, and if you didn't have the thumb issue you wouldn't really need it until then. With your thumb, though, it will be very useful much earlier.
Basically, you need to learn to move your whole hand when you move from 1 to 2, just enough so you don't have to stretch more than is comfortable/reliable. Not exactly a leap, but a bit like one. Hard to explain, but if you have a look at AJs Chopin 10/1 Project thread you'll get some good information and demo vids of what's involved.