Well as someone who owns a 3590.50 speedy, having zeroed in on that as the reference I particularly wanted to buy, I can tell you what I understand to be the case and I'm happy to be corrected if wrong. The transition to the 3570.50 took place I believe around 1996 and included an updated bracelet design which was the 1499 bracelet, different in style to the 1479 found on the 3590.50 (mine included). You can find some 'transitional' 3750.50 models with the 1499 bracelet that have a tritium dial with now yellowed lume plots before tritium dials were phased out entirely in 1997. These transitional models also came with the updated 3570.50 bezel insert that restored the accent above Tachym
ètre.
My speedy's serial, which begins 4829 is, based on looking the ilovemyspeedmaster.com date estimates around early 1994.
So, although not having seen any images of your watch, I'd be surprised if a 77x serial from 1999/2000 could be a 3590.50. If I'm looking at an original 3590.50 I expect to see as a minimum a tritium dial and hands, no accent above Tachymetre on the bezel insert and the 1479 bracelet.
It really depends what you wanted; for me these characteristics were some of the reasons why I was buying it so obviously had to be there. If you're just trying to determine exactly what reference yours is and you don't mind about anything else then it's of little consquence, especially the exact year of production.