If you are interested in vintage options which can be had in the $150 range and a 2 pc rod will work in your plans.
Fenwick FF-79, 8 ft, 6 wt, 2 pc and (IMHO) the best dry fly taper Fenwick ever made. Here you can see it performing on even a tiny stream catching wild cutthroats.
Fenwick FF-805, 8 ft, 5 wt, 2 pc. Great all-around rod that is not too strong for smaller streams but will cast a variety of flies. This would be a bit better than the FF-79 for big hoppers or throwing weight and fishing underneath.
Fenwick FF-806, 8 ft, 6 wt, 2 pc. This powerful and smooth rod will do everything you want and casts larger flies, streamers, and weighted nymphs, but you'd want to supplement it with one of your 4 wts for smaller water.
I think the FF-79 could go on a trip like that as your only rod, especially if you will be fishing the tributaries and not the big rivers.
Other options I'd recommend are:
Browning 322975, 7'6" ft, 6 wt, 2 pc
Browning 022975, 7'6" ft, 6 wt, 2 pc (lighter than most vintage rods at 2.8 oz)
Shakespeare FY-A250, 7'9", 6 wt, 2 pc
Shakespeare FY-A250, 8', 5 wt, 2 pc
Phillipsons in these lengths and weights but they cost more.
In any case, your instincts are correct about a 5 or 6 wt rod that is 7'6" to 8' in length. Others may offer a different opinion for certain unique rods, but I think that most of the vintage rods over 8 ft get a little loose. Can't speak to the more modern glass, however, as I don't have any...but you won't find them for $150. All of the rods mentioned here fall in that price range, and several can be readily found.