Like it or not, I think you should be looking at a S&W DA revolver. The M617 will have the best trigger for DA shooting and I recommend the 4" for overall use. Obviously you could choose a M17 or M18 if you found one. They are both classics and high quality.
The 5" M63 or an older 4" M63 might be of interest, but you will have to look for one. They will have a heavier trigger than the M617, but I think still pretty tolerable as they are pretty smooth.
Yes, I know, this is not what you want to hear.
The new Ruger SP101 is probably the closest revolver to your budget. You shot that one. The Charter Arms Pathfinder might be another but both will have heavy triggers and generally a little gritty.
An alternative is to find a Colt Trooper Mark III in 22 which has a slightly heavy but slick trigger in DA. It is a fine medium framed revolver and feels about like the S&W M617. Keeps your eyes open and you might find an old Trooper (original trooper) or Officers Model Target or Match, or Official Police in worn but very good shooting condition.