I just picked up a 20" GT Scamp which performance bikes has on sale in all its stores for $179 (REI had the same exact bike for 279.). it is a seven speed, with 8 out of ten of my own criteria. (low standover, proper brakes for a kids hand strength, gearing, <$250; slight curve on the handlebars (allowing better adjustment IMHO for growth than stem rise); etc. (the two criteria it didn't have were solid fork and hybrid style vs mtb tires, but 90% of 20" bikes I saw//researched didn't have that)

yes it it doesn't have your exact specs. But here are my thoughts and experience in case they are relevant.

- Reasonably priced non walmart/target etc 20" bikes are rare and sell very quickly on craigslist. The downside of that is that getting one used is likely to be difficult, but selling is going to be easy to recoup $50 to $100 if the bike isn't trashed.

- I think you can expect to get two years, not one. if like me you have a kid even younger you are looking are more like five usable years, but even at 2 years, $200 - $75 resale recoupe is just $65/per year. And a bike being 20% to small is an inefficiency easily tolerated by a kid, a bike being 20% to big is a danger.

- Don't sweat the common features that are all but inescapable. Like you, I started out absolutely opposed to a shock absorber fork. Fact is 90% of these bikes have them and kids are light enough that they have little negative "gushyness"

- pay more attention to quality brakes and properly engineered brake levers/handles that your kid can get good stopping power on.

- pay attention to actual stand over height. bring a tape measure and measure them from ground to right in front of saddle front. The specs on a lot of bikes change and a lot of published ones are WRONG. I was very happy with the 3.5" clearance we got on the GT Scamp. Kids this age are learning to mount and dismount from start and sudden stop and I observe this is important.

- fenders can be added to almost any bike. the GT scamp looks like it has holes for them. but fenders are for keeping your clothes clean in the rain. do your kids ride in nice clothes while in the rain that often?

Call a performance bike store near you, there summer sale has a few more days left. mine had 2010 scamps for $179 for 20" and $199 for 24 inch. They didn't have the 2010 in stock so they sold me the 2011 for $179. but the the 2010 looked identical in all parts and geometry.