Okay, so I finally got around to seeing what's up with this bike. I have confirmed that the freewheel is indeed a Suntour (I can see the Maeda stamping on the inner surface). Before messing around with anything else, I tightened the barrel adjuster a smidge, and the index shifting got a little better. A little playing around tightening and backing off the adjuster got the shifter working perfectly on the stand. I'm really happy with it now.
All I need now is to have the weather and my free time match up and I'll finally get it on the road. At least most of the snow has melted here (finally). I still need to get a small saddle bag, spare tube, and other accouterments for on-the-road issues and it's good to go!
Thanks for everyone for their patience and advice!! I'll post up some photos when I get it out of the basement and on the trail and road.