I'm going to go out on a limb and say that 4' drops with a $300 bike is probably a bad idea. I've seen these North Star bikes in Sun n' Ski Sports I think. With a price point between $200 and $300, I'd look at a used SS - maybe a Redline Monocog, a GT Peace 9r, maybe a good deal on a Raleigh XXIX - something along those lines.
You're probably not going to find a lot of used Monocog 29ers for sale. I live in Dallas and watch Craigslist pretty closely and there has only been two Monocog 29ers for sale on there in the last 2 months. That being said can only speak highly of the quality of the Monocog and Redline bikes in general.
I paid $450.00 for a new Monocog 29er last May. The other day I saw another poster that bought a new `10 for $360.00 at his LBS. Redline makes a great product so if you can find one try it out!
Boy, a bike that can take 4' drops at a $200-$300 price point is going to be pretty hard to find. I'll have to be the one to say look at older 26" wheeled freeride bikes/burly hardtails with a suspension fork. As much of a 29er mark as I am I don't think I'd pick a rigid 29er single speed for trailriding with 4' drops... Start hitting your pawn shops, bike shops that have used bikes, second hand sporting good shops and craigslist/ebay.
"I'll disintegrate over time if I expect my body to try to keep up with my mind" -BM
You can probably forget any 29er bike in that price range. You would have to build a burly wheelset to handle the drops which would not be cheap. Your best bet would be to look for a used 26" dirtjumper like a Giant STP or Specialized P2 for example.
I had a (1995 or 1996) Northstar La Luna that I bought for my daughter way back when. It was a Tange steel frame and was built a bit on the light and wispy side, but it was perfect for her as it was pretty lightweight. I also recall it having a 1" headtube, so that is always something to check for on bikes from that era ad sourcing a replacement fork could be problematic.