I believe Pachmayr still makes their Compac with the designation RB-J for this gun. Heavy, but it will mitigate recoil pain and allow you to maintain a solid grip in rapid fire...
The OP asked about Hogue Tamers but I have to agree with this. If you don't mind the extra bulk and weight, Pachmayr Compacs are hard to beat, IMO. I've used them on my Model 36 since they first came along and nothing really has improved on them.
But getting back to the Tamers, I have been wanting to try them on the 340PD. I finally found them in a local shop. Handy, since I've been forgetting to include them in my last couple of mail orders. Anyway, the Tamers made it onto the 340 today and were given a quick test fire. They are big, but not overly thin, which is what I usually dislike in Hogue rubber grips. They seem a bit lighter weight than Compacs, which is good.
They do a
very good job of absorbing recoil. I've always considered the 340 more or less unmanageable with 158 gr. .357 loads. I could fire 3 shots without having to adjust my hold on the gun - something I've never been able to do with the factory boot-grip. It would be hard to say so for sure until more rounds are fired, but the Tamers may just end up on the 340 permanently.
My only complaint about the Tamer design is the threaded rod and nuts that retain the "butt cap," as Hogue calls it. I am pretty patient when it comes to assembling things that don't just fall together. In spite of that, I had to give up on the two retaining nuts and just use the screw by itself. I suppose Hogue wouldn't recommend that but so far the Tamer is working just fine without the nuts, and I was able to avoid throwing Tamers, butt cap, and revolver out the nearest window, which is where I was heading with the nuts.
The Tamers seem to have sufficient clearance for speedloaders, but since I don't use them, someone who does might disagree. If the butt cap design proves trouble-free, and it probably will, I think the grip will be a winner. It's the only thing I have seen that gives the Compacs a good run for their money.
Some weights of various J-frames lying around:
340PD, empty, with Tamers - 12.10 ounces
same, with 5 Winchester .357 Silvertips - 14.93 ounces
M442 electroless nickel, empty, with Hogue Bantams - 14.57 ounces
same, with 5 Federal .38+P 139gr. Hydra-shoks - 16.87 ounces
M640, empty, T-grip, and smooth S&W magnas - 21.28 ounces
same, with 5 Federal .38+P 139gr. Hydra-shoks - 23.58 ounces
Model 36, empty, with Pach. Compacs - 22.45 ounces
same, with 5 Winchester FBI loads - 25.18 ounces