Get a stout bullet that doesn't have a soft front end and let the rodeo begin.
What bullets would those be exactly in .243" ? I've killed deer with 100 gr. interlocks, 100 gr. core-lokts, 100 gr. power shoks, 95 gr. SST's, 85 gr. Sierra HPBT and didn't find any to be overly "stout". In fact I've recovered examples of all those bullets from deer and all were anywhere from "well and fully mushroomed" with significant weight loss to "well and truly fragmented" in bits and pieces.
