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In all cases I carry a set of "Tyre Pliers", plug kit, core tool and spare cores, spare complete stems, tubes, patch kit and the compressor is supplemented by a manual air pump (which I pray to God I never have to use to inflate a tire!!!). Ratchet straps help immensely seating beads. Note I run steel "tube-type" steel rims so they don't have the dreaded "safety bead" feature that makes breaking a bead near impossible without a tire machine. Drive over these tires (with valve core removed) and the bead breaks just fine.
For people that do not want to carry (or do not have when they need it ) a Tyre Pliers bead breaker;
Field bead breaking is normally fairly easy simply: remove the valve core. get out the jack and position it between the tire(on its side) and the frame/bumper with the base of the jack touching the rim; then jack the bead off the rim.
Hi-lift jacks are good at this hydraulic jacks less so.
Once started step on the tire near the area where it has initially pushed past the safety bead, you can normally push it off by "walking" around the tire....
If anticipating field tire changing I carry a pair of tire irons ('way easier to use than jack handles, large screw drivers, separated spring leaves or pry bars) along with a drilling (smaller/more packable) or blacksmith's hammer (larger).
Depending on the expected terrain and accessories; I would opt for a front bumper carry assuming that terrain approach angles are not a concern.Any thoughts on where to carry a second spare on a Ram 2500, 8 ft box with FWC Grandby? Front vs. back.

Excellent point. The experienced Baja guys bring a good unmounted tire in addition to the stocker on smaller rigs.Not necessarily a spare tire mounted on a wheel, but just the tire and use the tire to carry things inside it to save space and weight.