I figured as much. I did buy the astigmatism correction add-on, but I haven't found it has helped as much as I would have thought, especially at this throw.
There are two main focal planes you need to consider when using prism lenses: vertical and horizontal. Prism systems don't change the vertical focus of the projector, bit they do change the horizontal focus. An astigmatism corrector adds optical power to the horizontal plane to "bump" it a little so that it's plane of focus co-incides with the vertical.
Fixed astigmatism correctors have a definite sweet spot at which they work best. After all they are "fixed", by definition!
At short throws, again you are correct, a fixed astigmatism corrector needs to be very close to ideal to give you best focus. At longer throws you have some more leeway.
To give you an idea of sweet spots: the original Panavision prism lenses, from the early 1950s, had a set of tables for determining the best astigmatism corrector to use. These tables started
at a throw of 72 feet
, and then up from there. Short throws like 13 feet weren't even considered.
The corrector lens won't fix color aberration at all.
A throw ratio of less than 1.5 is a challenge. You'll need a biggish lens, which isn't going to be cheap. Sorry, can't make any suggestions, but I'm sure others here might be able to help.
Glad you found the pincushion calculator useful. I wrote that a long time ago, but the numbers live on!