I used to put a lot of the 240 grain .430's through a Charter Bulldog. But that gun had a very smooth bore, which is important for leading, and I used only very light, slow loads. In that arrangement it would print about 1.6" at 25 yards, believe it or not. Pretty good for a 3" fixed sight gun. But it did put them about 8" high and 2" left, IIRC. Still, it grouped them.
I also used these in a pinch in .45 Auto for gallery matches (50 feet). They could clean a slowfire target at that range. Again, light loads. Probably in the 650 fps range in both guns.
In your shoes, I would start the .38 Specials with a load normally used for wadcutters. Perhaps 2.7-3.0 grains of Bullseye or its equivalent. See if your bore condition produces leading issues with them or not before increasing the charge weight. If you have leading issues at those low pressures, firing them warmer will almost certainly make them lead more, though I have run into exceptions to this, as when the cylinder throats were no wider than the groove diameter of the barrel.
If you have a leading problem, you may want to consider light firelapping of your gun or at least buffing the bore with some JB Bore Compound or Iosso Bore Cleaner. You can "fire polish" by rolling a couple dozen bullets in JB and shooting them with just a couple grains of powder and a tuft of polyester pillow filler over the charge to keep it over the flash hole, then cleaning the gun after every six. These are real catsneeze loads, but you just barely want the bullet to be spit out. You can see these streak through the air on a sunny day. Makes for interesting feedback if you ever choose to experiment with point shooting and prove the value of sights to yourself.