This one is not going to be easy.
You already know about the screw-mount (M-39 or LTM) Leica bodies that will just meet your financial specification. At the risk of being yelled out of this thread, I also point out that there are several copies and derivations of the Leica LTM camera bodies made in Russia and Ukraine that will also do the job for you, while also costing significantly less. Even the FSU lenses should not be overlooked. Yes, many of the Kiev, FED, Zorki, and other similar bodies probably will need a CLA, but even a Leica IIIf or IIIg also will need one by now.
I do agree that the FSU cameras do not have the finish nor the smooth operation of a Leica or Contax, and they have the quirk of requiring that operation to be performed in a very precise order each and every time to avoid possible need for repair to put things inside back in order, but they certainly can do the job when we see what is on the print.
And, while I do not have a Leica, I do have a Zorki-4, a Zorki-4K, and a FED-2c. The lenses include the Jupiter-8, Industar-26m, Industar-61, and Helios-44-2. You did say that you wanted to hear opinions of experienced users. I prefer the Jupiter-8 and the Helios-44-2 on the Zorkis, but the FED does have that long base rangefinder that helps when you have the lens and camera adjusted together.
The other rangefinders here include fixed lens models from Minolta, Yashica, and Konica, although there may be some that I have failed to list. My favorites in those are the Minolta Hi-Matic 9 and the Yashica Lynx 1.4.