It appears throughout that each of Frasier's tapes are for a single episode of his show and all the tapes are in one cabinet. The tape that Frasier puts away claiming to be his 2000th is actually the 841st tape in the cabinet. In fact, it's the 840th tape! there is one tape missing in the lower right corner.
The cassette that Frasier has in his cabinet are of a type that typically have 60-90 minute capacity per side. And since his radio show is three hours long (180 minutes). One tape wouldn't be enough to store even one show. Much less the more than three per cassette that would be necessary to fit 2000 shows on 649 cassettes.