If you're searching for .44 Special cast bullets? Search for .429" bullets.
Midway lists 200 grain .429" hard cast. Montana Bullets lists a 210 grain SWC at $26.35 per 100 or $126.75 per 500. Best to buy components locally though.
"...thought lswc was..." It is.
The bullet shape doesn't matter much for hunting. How accurately you can shoot 'em out of a wee thing like a Bulldog. My boss that the shop I worked in long ago had a Bulldog. Cracked the factory wood grips with a 265 grain blaster load.
"...trade some weight for increased velocity..." A cast 200 grain load doesn't go very fast out of an 8" test barrel. Max loads with some powders run a tick over 1,000 fps. You won't get that out of a stock BD barrel. Even if your's is one of the 4.2" "Target" models.
Work up the load for accuracy, not velocity. Oh and the boss fixed his grips with Acraglas. That was before civilised people could get Pachmayr grips for a BD. snicker.