If you have it where you add a provision to the bylaws stating that to
be eligible to vote in the annual elections, all dues must be paid no
later than 5 business days before the date of the annual meeting, that
may fix some of the issues. Yes, you'll have to verify membership
status, but wouldn't you have to do that, anyway? By having a deadline
for registration tied to voting eligibility, there would be enough
time to process registration and update the roster.

Again, this would have to be an amendment to the bylaws. With adequate
notice and communication, however, the majority of members who would
be attending the annual meeting are likely to comply with the
deadline. But if you feel that anyone who wants to pay their dues at
the annual meeting should be allowed to vote, then you just state that
all dues must be paid by the start of the annual meeting. Late
arrivals would not be eligible then, but we can't bend over backwards
to accommodate every possible situation.  We have to agree on a set of
simple rules and we have to accept that they will not be accommodating
to everyone and not everyone will like them, but that's the case with
every organization that's currently in existence, with the possible
exception of the Distinguished Egalitarian Society of Professional
International Sectarian Existentialists (DESPISE).