I think most pick ups would in the past take a quad, i've loaded them onto a couple but that would be 20 odd years ago and quads were a lot smaller then and before double cabs really existed, have to admit not done it since but do see it occasionally.
(ur 350 big red was ur standard honda, now all 420 or 500, ur yamaha'a are all 700cc and all wider and longer than they used to be)
Most double cab pick ups back tub is less than 6ft long some only 5ft so would need tail gate down with quad wheels on the tail gate supporting wieght of bike.
The simpliest way would be a trailer as already mentioned, handy for loads of other things too.
Or take the back tub off and put 1 on that suits u and wot u want, but if u lengthen the back tub, remember most pick ups are already 15ft odd long before u start and with the turning circle/parking ability of oil tanker. So not very handy if u ever use it about town when ur not stalking