According to
this the oldest Trek 1000 is from around 1986 not 70's. A 87 catalogue from the same site shows it is a
12 speed, but it might have an ultra 6 freewheel so the rear dropout spacing might be for standard 5 speed and why you are running it as a 10 speed. I think this is quite an important issue to check (i.e. what the rear dropout spacing is, whether it is 120mm or 126mm, corresponding to 5 and 6 speed respectively). It is important because a) one really shouldn't try to force a wider hub on an aluminium frame, and b) the choice of 5 and 6 speed freewheels is vastly different.
Either way, with Campag parts it is probably worth maintaining as much originality/period correctness as possible, and to achieve that it is easiest to change the freewheel for a lower geared one if possible. If the rear spacing is 120mm then you are constrained to pick from 5 speed freewheels, depending on what the largest sprocket is there currently, a new one with a 28T sprocket (which are commonly available) might offer adequately lower gearing if what you have now is a closely spaced racing cluster, if not you might have to look for rare freewheels such as
this. If the rear spacing is 126mm, the choice is much greater and freewheels with large sprocket up to 34T are
readily available, but you will likely have to change the rear mech to adopt something like that. A larger large sprocket at the back will likely require a new, longer chain.