Have you considered putting a tritium sight up front? To me, one of the great advantages of the shrouded barrels on these guns is the ability to easily install aftermarket sights (not that there is a huge selection for the J-frames, but there are a couple).
Countless times I have heard people extol the Airweight series .38 +P guns as the best carry J-frames, or anyway the best value out there. I agree that revolvers like the 642 and 442 are wonderful snubs, but the issue of replacement sights tips the balance for me in favor of the .357 scandium/titanium models (I do acknowledge that the tritium-sighted M&P 340 is now out, essentially making it an Airweight .357).
Sounds as though your impressions of the .357 round from this gun are about on par with many others'. Too much, at least for confident defensive work.
This brings up something else. An argument made by the "642 club" in favor of the Airweights over the Airlites concerns, of course, the caliber issue. When someone is considering a 340 or one of its brethren, frequently there will be a flurry of sober, and sometimes histrionic, admonitions about how "it is impossible to fire .357 out of it anyway, so why not save money and get an Airweight?
". From when I first started researching the 340PD, let alone using it, I've never regarded it as a .357 - simply as a very strong .38 +P that happens to have the additional enticement of being several ounces lighter than a 642 or 442. This is not to mention the sight issue already discussed.
With the above three improvements on the Airweights - weight, strength and night sight capability - the choice was a no-brainer in my case. It just seems that not many people attach the same importance to these issues, particularly sights.