yup. you have to change out the internal cd changer. there are 2 types. the key is on the face of the unit, you will see the 6 disc cd changer label. most of the units will also have the 6 buttons on the lower part, 2 rows of 3 each. also, the plug in connections on the back have to be the same. here is a unit i recently bought, and took out the cd changer:
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&category=48612&item=120004247717 i also got one that was for a miata, and another that was in a 626. the key is the 6cd changer on the face, and the plug pattern on the back. the later units have a different plug configuration.
you have to take the unit apart to change the cd changer. but it is really easy. after pulling the unit out of the car, take off the spring clips on each side. they might be really ON there, and you might have to use a hand impact, or even drill them out. watch out, because the screws holding on the clips are countersunk, and hard to get. now take off the top cover, 2 screws on each side, at the end opposite the front panel, then the cover will lift off. now remove the front panel. 4 screws, 2 on each side, then gently lift off the front panel. the changer is held in by 4 screws, 2 in front, covered up by the panel, and 2 in the back. disconnect the ribbon cable on the right side, it just pulls out. now you can lift out the changer.
the hard part will be finding another changer. here is one on ebay that has been there forever. 200 bucks used is a ridiculous price, imho.
http://cgi.ebay.com/ebaymotors/CASSATTE-CD-PLAYER-CAMBO-6-CD-1999-MAZDA-MILLENIA_W0QQcmdZViewItemQQcategoryZ43981QQihZ002QQitemZ4628697686QQrdZ1QQsspagenameZWD1V here is one just like the one i got. the problem is that you dont know if the changer is fubar or not. the ones i got were brand new, and the changers were never used.
http://cgi.ebay.com/ebaymotors/00-01-Mazda-MPV-6CD-CD-6-Disc-Changer-Indash_W0QQcmdZViewItemQQcategoryZ43948QQihZ003QQitemZ130029002039QQrdZ1 price is a lot better, but the early changers were kinda fragile. we have 2 99's, both have the bose units exactly like you have in the millenium edition, both with brand new changers, and i even have one new changer as a spare. it might take a while, but ebay is the best place to get them. otherwise, it is the repair shop(i was quoted 500 bucks), or a new unit from mazda-you can get a bose unit w/6cd changer for a 626 that is identical for about 660 bucks.