As much as we might hate it, on the balance of odds, Bush probably did win in Florida...
No, that's incorrect. Based on what we know, it's pretty clear more Florida voters preferred Gore, intended to vote for Gore, and thought they had voted for Gore. the reason Bush was declared the winner wasn't that more people voted for him, it's that for a variety of reasons (some legitimate, some illegitimate) a large number of votes for Gore didn't get counted -- enough to lower Gore's vote total below Bush's in the first counting.
Some of those lost votes could not have been recovered even if there had been a recount. For instance, a large number of votes which people thought they were casting for Gore were miscast because of the confusing layout of the butterfly ballot. It's pretty clear many of those votes which were recorded as votes for Pat Buchanan were actually intended to be votes for Al Gore but there's no way of knowing which so that can't be corrected. Those votes for Gore are legitimately lost and no recount will change that.
But the overcount votes are a different story. Many people voted for Gore by filling in the box next to his name, but also wrote in his name on the line which said to fill in the name of the candidate you wanted for president (i.e. the write-in line) because that's what a literal reading of the instructions on the ballot indicated they should do. That was a mistake on those voters' part -- they didn't need to write in Gore's name as well as filling in the check box -- but it's a correctable mistake because the voter intent was clear so by Florida law those were valid votes for Gore. Those votes had been discarded in the original count because the counting machines saw both a check-box filled in and the write-in line filled in and automatically discarded those ballots, but a human being rather than machine examining the ballots could easily see those were valid ballots and would have seen it if a valid recount had been done. (Only ballots where a voter checked the box for one candidate and then wrote in the name of a different candidate should get discarded as overvotes.) And there were enough of those mistakenly-discarded ballots to have brought Gore's vote total higher than Bush's, which would have reflected the actual intent of the electorate.
The Republican strategy in 2000 was to find as many ways as possible to get Gore votes discarded in order to be able to make Bush the winner -- in other words, not to win the election by convincing more people to vote for their candidate but to win the election by getting more of their candidate's votes counted and more of their opponent's votes not counted.
That kind of thinking is very harmful to a democratic system, but unfortunately it has become increasingly common in the US in recent decades. The GOP especially has engaged in many efforts to suppress votes of people they think are more likely to vote Democratic, to make voting slower and more difficult in areas that are heavily Democratic, and to find ways to discard votes which they think are more likely to be Democratic than Republican.
In 2000 the Republicans were able to get enough Democratic votes discarded at various stages of the count and recount -- and to prevent a careful recount -- because their intent was not to get an honest representation of how people had voted in the election, it was to get their candidate elected regardless of what the actual outcome had been. But the actual outcome, if we're talking about the will of the Florida electorate rather than the result of game-playing to see which side can get more of their votes counted and which side can get more of their opponent's votes discarded, was that Gore was Florida's choice for president in 2000.
