The case shape remained pretty static from the 60s onwards so an 1171 should fit a 3570, often though the 633 end links on those need a little fettling even when new, they are hollow so can be adjusted pretty easily though. I have seen 1171s that just fit, and others straight out the packet that need some gentle persuasion. A 70s 1171 will probably be a bit tired and rattly but the upside is that it probably wont need too much work to make fit as there will be slack.
Another option worth considering is one of the various designs that Uncle Seiko and Forstner offer. Those are pretty similar quality to the Omega originals (that is to say good but not great) but rather cheaper. They even do a 1171 repro I seem to recall along with many other classic designs.