I have only been aside in clinics, so I am no expert, but I will second the idea that you might actually want–and be safer in a standard side saddle.
The left leg presses into the leaping horn and helps to keep you on and stable. If you were to ride offside and your right leg is not able to do that, it would be akin to not having a leaping horn–which means the only thing keeping you on is your knee hooked around the horn.
In the last clinic I took, the first saddle they had me in did not fit me correctly and made my left leg basically useless–meaning I was hanging on by only my right knee. It was terrifying. Once they got me in one that fit correctly and I could use that left leg, I was cantering off with a smile on my face.
You might also want to consider a “western” side saddle. There are companies recommended by the ASA that make modern western style ones (Crest Ridge). There is no one who makes modern English style saddles that the ASA considers safe–many of them are knockoffs made in Asia and though they look the part, are really not functional at all. The western saddles also have deeper seats, while the English ones are flat. Western side saddles do not look like Western saddles and, though they are not reinforced for jumping, are quite comfortable, IMO.
All that said, it IS possible to find offside saddles…and even to move the horns in some cases. If you don’t hear back from the ASA, drop me a OM and I’ll put you in touch with my clinician, who just happens to be the president. She is wonderful and very knowledgeable.