Can't reply on your specific year, but maybe the following would help:
Our 79 Scottsdale K10(4wd), with a 350(5.7), auto 3-speed and towing package, pulled a 4100lb Mako boat/w trailer for 15+ years with absolutely no problems. The original tranny is still doing just fine.
Our 97 Suburban c15(2wd), with a 350(5.7), auto 3-speed w/od and towing package, has been pulling a 6200lb Travel Trailer, and a 6300lb Bayliner Cierra boat/w trailer since almost new, with no problems. Granted, 18 years newer, but figured I'd throw that in.
I never tow in overdrive, and if in the mountains, which I have been with the camper, I will manually shift if the transmission begins to "hunt", i.e. shift back and forth between gears.
zieg85 is correct about the engine/trans/rear end gear ratio dictating towing capacity. However, pulling 3000 plus a 650 dolly, with a light bed load, IMO, should be just fine. Just make sure the tongue weight is not excessive.
I dont' know the weight of your "dual axle cabin trailer", but they can get very heavy by the time you get them loaded. No way to know how much weight you were really pulling on 177. The actual weight you were lugging up the hill might really surprise you.
Hope this helps a bit.