Have several countries use more Cobalt or other cladding to drastically increase the duration of fall-out. Coupled with the major powers not downgrading the size of their warheads as accuracies improved in the 1960's and 1970's. No SALT agreements so by say ~1985 there are a lot more missiles and warheads, which are larger and more lethal. Add in a few more nuclear powers, say India builds up a force after its test in 1975 I think it was and Pakistan responds, plus races elsewhere.
In that case it would probably be centuries at least before humanity starts to recover anything like modern civilisation. Not to mention the possibility of extreme religious cults say opposing the evil of technology, diseases possibly running rampant in a rump population weakened by hunger and radiation.