I don't think you will find an amp under $350 that will accomplish your objective, but I could be wrong. If you want something light in a single rack space checkout the Stewart World 1.2 new there about $650 used on talkbass they go for $400-$500. Also you are going to need a preamp and you need to make sure that the preamp can significantly push the power amp to get maxium output. You more than likely want a power anp that can run bridged and parallel and can take a 2 ohm load. That's asking a lot for a budget price. Checkout Crest CA9 or a CA6 Stewart also makes a 1.6 and a 2.1 there is also QSC power amps. Preamps there's Demeter, Alembic, Aguilar, BBE, and Kern a good power amp and good preamp could run about $1200-$1500, but you'll have plenty of headroom with the right combination. Hope this helped.
Good luck.