I totally believe in using busses for mixing, my studio is set up around that as well. I have eight busses, but eventually want a 16 or 24 buss board.
Using direct outs is not anything like bussing tracks. If you are assigning tracks to busses, those tracks most likely have levels and eq already set before they are bussed, plus fx sends. Once the tracks are bussed they often go to more processing, like compression. Busses are like submixes, very different than sending a signal out the direct outs, which is usually pre- everything on the channel strip.
$1,000 is really pushing it for a 16-24 channel mixer with 8 busses. I think that the best option might be to find a used Mackie 8 buss series, a Soundcraft Topaz, or perhaps one of those Tascam analog mixers. The Tascam 3500 might be too pricey, but there were other smaller models. Used analog boards are pretty cheap these days, but you really have to check them out very carefully with a fine toothed comb before buying. Only buy a used mixer that you can inspect in person. At least that's my advice.