This is the sort of situation where the realities of those older machines show their limitations.
A schematic shows two 6973's in push-pull (prob class A-B) in each channel. With both channels driven you'll see 12 watts rms at-best and 8-10 watts is more likely given wear and available B+.
Bose, and most other compact hi-fi speakers are very inefficient and this becomes obvious when compared to the P.A. type speakers used in a juke. Without getting to into the weeds of the decibel/power relationship the reality is that if the Bose speakers were only 3 db less efficient then the juke spks. they would need twice the power in watts to equal the loudness of the machine speakers -Bose speaks are more on the order5-7 db less efficient.
Another factor is the tone quality of the original pickup and how the amp is tailored to flatter it and the machine speakers. Very often the sound will appear dull and 'woody' when passed through better speakers. The higher distortion of a cheap pickup will be more noticeable.
What might be a good alternative here is to tap the volumes control and take a feed to the amp/speakers of your choice. There at least you can choose an amp adequate for the purpose and shape the tone somewhat better for that system.
Schematic:
http://www.verntisdale.com/schem/414-18.jpgGood luck whichever you choose.
Rob/NYC