mtrude
it sounds like that 357 did exactly what it was supposed to do, the bullet exited, the deer died, from a single gunshot. Somebody is bound to bring up the fact, the hollowpoint bullets might have left to a larger blood trail, but I will point out right now, that extra expansion, comes at a cost of lower penetration, and your deer might, repeat might, have dropped faster with a hollowpoint but I doubt he would have got an exit wound.
My brother-in-law Hunts with 357 mag marlin Carbine. He tried hollowpoint bullets, and immediately went back to soft points because the hollowpoint's did not exit. As you get more experience with a handgun, you'll find several deer can be hit/shot identically with the identical ammo and your results will vary. From the evidence you given, I would stay with the load you are using presently, and look forward to many more dead deer.
I use of 445 supermag, the 300 grain bullets I use are pushed between 1200 fps-1500fps I normally get a very good blood trail, and a good exit wound, but even with more than twice the power and more than twice the bullet weight, I occasionally get a deer that runs. Granted the distance is usually very short(10-30 yd.s) but you're not going to get the kind of results you'd get useing a high velocity rifle like the 257 weatherby magnum(deer collapse of the shot) when you're using a handgun, using a handgun is a little bit more like archery in that it takes a few seconds for the deer to bleed out. So I repeat. Your results were excellent, your,shot was excellent, you did everything right, you got very common results for the equipment you used, going to larger caliber, will tend to shorten the blood trails. But going to larger caliber handgun is not likely to get you better results on deer. It's hard to improve on a single shot and dead deer!