A 44 Special will push a 200gr jacketed bullet ~850 fps while a 44 Magnum will push that bullet to ~1450 fps. Since you said you are looking for a compromise between the two I would think a 200gr bullet ~1100 fps would probably be a good choice.

The Speer Gold Dot 44 Special uses a 200gr GD bullet listed @875 fps. Their 210gr 44 Magnum is listed @1450 fps. Their Short Barrel 44 Magnum uses a 200gr GD bullet reported @1075 fps, just what you seem to be looking for...

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