If turntable connects by RCA cables then you are in good shape. Just plug turntable into inputs of the little preamp suggested by Alec, and then get some short (12 inch) RCA male to RCA male extensions and plug them into outputs of preamp and RCA jacks where phono was formerly connected. If you have a ground wire from turntable it is probably connected already, through the plastic plug that you described.
This unit will not be HIFI, but it will probably sound OK. If sound is too bassy you can put a capacitor in series with phono input on recever and use that to roll off the low end a little, or maybe just use your tone controls. Usually, straight up position of tone control is close to flat, but might be different for your unit, and also, there may be a frequency contouring network on volume control or elsewhere in unit. You will just have to scope it out. Years ago, I modified a Zenith table radio to add highs to the sound by modifying the contouring network, and cleaned up sound considerably. This unit will be prime for a few small modifications like that to make it sound better.
I think the N665 designation applies to stylus rather than cartridge. Usually, "D" designation means that stylus is diamond, as opposed to "S" for sapphire. You might try Googling the N665 designation, and the 906 designation, and the 83D designation. Also, it might be worth your while to dismount cartridge completely, and if there is a clip that holds it, take the clip off. You might find a manufacturer's model number.
Where are speakers? Are they in the bottom of cabinel and pointing down? This may be the reason they are muffled. Also, if there is a tweeter or midrange speaker, it may not be operating properly and need replacement. If this is so, then it is probably an easily obtained inexpensive phenolic ring tweeter or some sort of inexpensive cone driver. I don't think this unit has a hugely expensive speaker system, so repairs and modifications will be easy and noncritical. The one problem I foresee with a magnetic cart is the possibility of acoustic feedback at low frequencies cause by the 20 dB additional low frequency gain from preamp, and additional bass caused by improved low frequency response of magnetic cart, combined with placement of speakers in the same box as phonograph. Many years ago, I replaced the ceramic cartridge in a Califone record player with a Shure M44 and inexpensive preamp and lows increased considerably, even with open back speakers.
And good luck from the old modifier and improviser,