It was a VERY messy situation - legally.
The Gore campaign made a MASSIVE political mistake which set-up failure, requesting hand-recounts in only heavilyy democratic counties. They lost the public argument about ensuring 'every vote is counted' from that point on. Gore should have asked for a state-wide hand recount.
The Bush argument was based, as you say, on the 14th amendment - namely the different standards being applied across the various counties was a violation.
Gore argued that there was a standard, the 'intent of the voter' issue - which I thought was shaky legal ground. However, where Gore was on firmer ground was the concept since with under/over-votes on punch cards there are often calls for a subjective call to be made on a card... then there is in effect different counting standards across the country, and if the count was unconstitutional on those grounds, then every other election that used different standards within a jurisdiction was also invalid.
The other issue was the 12 December cut-off for the votes to be received - to fit within the '6-days prior clause' - as the electors were due to meet on 18 December.
The legal remedies the USSC put in place, I felt were the issue, rather than the legal arguments. Since they decided that no legal recount would be completed by 12 December... they allowed the current certification to stand.
In my view, the Court should have stood by the Florida Supreme Court and done two things...
1. Order the Secretary of State to push back the meeting of the electors to December 22, which would have given them another 4 days for the Florida Supreme Court to determine a standard and undertake the recount.
2. Order a state-wide, manual hand-recount.
Which was the position of Justices Breyer and Souter
As I said, I don't have an issue with their legal decision, I do have serious issues with the form of their remedies, which I do think showed a politically driven desire to see the count ended in Bush's favour.