In this case it matters less what the founders intended and more what the framers of the 14th Amendment thought almost 100 years later. You can read in Richardson v Ramirez a bit of a history of felon disenfranchisement; a reasonable summary might be: "there was a lot of haggling over the specific language of the clauses of 14A, but disenfranchisement for crimes was a consistent point of agreement".

Of course, that doesn't mean that it's right to disenfranchise felons (it almost certainly isn't), nor does it mean any state is obligated to disenfranchise (most states don't). It does however mean that it's not straightforward to appeal to the Constitution in arguing to get rid of it.