You'll have to pardon me here, but anyone using a 135 gr. Gold Dot for a handload must be contemplating at least the possibility that it could be used in a defensive application. Try to keep things in perspective. SPEER is only interested in your ability to replicate ballistics. It is obvious that they are not considering an actual defensive application. Power Pistol will obviously get you the right numbers as far as velocity, but that is only one part of the total equation. For a defense load, PP is about the last powder I'd choose for this. Blue Dot will get the numbers you're looking for, but I ain't gonna use it, either; even though I've burned more Blue Dot that any other handgun propellant for 25 years now. It doesn't fit the application for a defense load powder. If a flake powder was the way to go, you'd probably be better served by Unique in this case.
One thing anyone should do besides look at the manual when developing a defense load is to do some night shooting, or replicate it by shooting at an indoor range.
KODB: JFH is making a very good recommendation here with AA#5, considering the performance level you're looking for. #5 is a very low flash powder and works well with cast loads. You should easily be able to get your performance requirement with the 135 gr. Gold Dot, as well.
If this is really about a single powder working well for both cartridges, as well as many others, Ramshot True Blue will cover all the bases as well as any you'll find. Not necessarily in this particular order, but considering a compromise with these variables: Accuracy, velocity (as outlined), economy, and minimum flash and probably the lowest standard deviation numbers you're likely to see from the powders mentioned. Anything you can do with Unique, you can do with True Blue and get minimal flash and better ballistic uniformity in the bargain.
I don't have data for the Gold Dot, but looking at Ramshot's data for a 140 gr. Sierra, 5.3 grains (Listed as max) of True Blue achieved 916 FPS with a standard deviation of 8! Single digit SD's are not that easy to come by. Now, the reality: the results were achieved with a 7.71" ballistic test barrel. Your velocity will be lower, but here's the good news, the pressure for this load is 15,945 PSI; over 1000 PSI below the max for STANDARD pressure .38 Special (17,000 PSI). You should be able to bump the charge by looking at +P data. I feel pretty comfortable in saying that you should have no problem getting 950 - 1000 FPS in your 4" revolvers with the 135 gr. Gold Dot. You might even get to 950 FPS without going into +P pressure, and even then, today's limit of 18,500 PSI is mild enough to eliminate concern for the M10.
Only the newer manuals will have data for True Blue, but it's worth the trouble to get your hands on one. Ramshot's Start Charge for .357 Magnum and the same 140 gr. Sierra is 8.0 grains to achieve 1075 FPS and since the velocity was obtained with a 6" barrel, you should be very close with your 4" 686. That's considering that you'll actually be using a 135 gr. Gold Dot. In the past, I know that the Ramshot Ballistician used a 6" 686 to chronogragh velocity for testing of Accurate Powder's load data. My personal loads were warmer at around 1200 FPS from a 4" M19. There may be one inconvenience, but with a powder this dense (which will meter exceptionally, btw) and the lower charge level, I'd follow the recommendation to use a magnum primer for .357 loads, the only standard primer I'd use here would be the CCI-500. In .38 Special loads, standard primers are fine.