That's about the time frame that I was making most of my boards -- late 1980's up through about 1998. At first I used AutoCAD to layout the artwork (since as a student it was free -- and this is back when it came on two 5.25" 360kB floppies). In about the 1994 time frame I graduated to Protel (version 2.something). I tried the autorouter a couple of times and was completely disappointed with it. Every board I have ever laid out has been 100% hand routed, including some boards I did for Boeing that had 3000 pads. Takes a while, but you know that what you get is what you meant to get.My projects were wholly avocational (and, hence, not time critical) then too 'twas the early 1990's when services such as you describe were both scarce and rather difficult to 'find'...
I've tried other PBC layout tools since and I still keep coming back to that old Protel v2 software that was written for Win 3.1. All the newer stuff just insists on doing my thinking for me.