Alternator hesitant when first starting

[AAXD]

When I start my 97 Disco, the tach sits at about 250rpms for between 5 seconds and a minute before it finally gets up to speed. At first I thought I had a bad bearing so I lubed the crap out of the front bearing and rear bushing hoping this would help. When I removed the belt I spun the alternator and it spun maybe 2 turns before stopping. Normally it should spin freely which led me to believe it was a bad bearing or bushing, after I lubed it it spun freely but the tach is stil very hesitant and takes a while before it will spin up. When it does it happens fast and jumps right up to idle speed and there is a slight whining sounds like the fan inside is spinning faster. Could I just have a bad bearing or could it be some kind of electrical resistance causing it to do this? I'm not particularly worried right now beause it always comes up to speed but I'll need to replace my almost brand new serpentine belt soon as it is just running over the pulley that is not spinning at the same speed and there is some melted rubber on the front of the alternator. I'm going to order a rebuilt alternator just to be safe but I'm wondering if I should keep my old one and have it rebuilt and keep as a spare or send it back and get the $100 dollar core charge.

[Disco]

Personally I don't think it's worth keeping the alternator as a spare unless you do a lot of off-roading or drive in isolated areas. The rebuilt one should last for quite some time, so lugging the spare around seems pointless, but then you can never account for "Murphy". Take the $100.

[roverX]

I sat carry a spare if you can do without the 100 bones.