Earl,
There are pretty good odds that the Il-2 shot down a few enemy fighters with its main guns, but I still wouldn't consider it a fighter. Both the SBD and D3A were tasked with CAP missions when there weren't enough F4Fs or A6Ms to spare, yet neither ought to be considered a fighter.
The A-1 was a great attack aircraft, but it really cannot be considered a fighter-bomber. It completely lacks credentials in the fighter part of that role. Even if you give it the benefit of the doubt on that it would still not be the best fighter-bomber of all as while it does very well on the bomber part of the role it is very weak on the fighter part of the role. To be considered the greatest fighter-bomber the winning unit needs to be able to do both roles effectively, not just sort of on an emergency basis when pressed into it. The Spitfire LF.Mk IXe/Spitfire Mk XVI is probably a better balanced fighter-bomber than the A-1 is.
The Fw190, F6F, F4U, P-47, Typhoon and Sea Fury are examples of single engined aircraft that could do both roles, being competitive with their contemporaries in the fighter role while still being effective attack aircraft. The A-1 was simply not remotely competitive with its contemporary fighters in the fighter role.
Realistically this means the best prop driven single engine fighter bomber is almost certainly going to be a late F4U or the Sea Fury simply due to the fact that they were the end of the line for prop fighters. If were pick the best based on its capability related to its fighter and fighter bomber contemporaries the question is a lot more interesting.