This is seemingly an old thread, but I'll add my two cents.
I'd carry a Hi-lift Jack & 'normal' winch recovery kit
https://mechanicguides.com/best-farm-jacks/ plus a winch extn strap before I'd carry a hand winch & that bloody great lump of winch cable roll!! But a Patrol door is NOT the place to mount it for more than a few weeks. You can swap the brackets to hang it off the INside of your roof rack; or just slide the lift head off the bar, pull the handle out of the lift head, & stash the disassembled parts somewhere easily accessible in the back of the vehicle, or under the middle row of seats (if there's nothing else there & you can readily get it all out if you do get stuck)
For those not in the know, - Hi-lifts aren't meant to be used for tyre changing (altho you might need to use one to lift you vehicle high enough to put a proper 'tyre changing jack' under the vehicle!
) Buuut, you can buy relatively cheap attachments to fit your wheels so you can lift one at a time to pack under it to regain traction; others that fit your bull bar to lift that end; your tow bar receiver hitch will work up the back; & good rock rails or sliders will let you lift one side - giving you places at all 4 corners (wheels) to lift as well as each side & up front & back - meaning you'd have enough lift points to remedy any one bogged or traction less wheel, lift one side to regain traction or un-bog, or move the front or back sideways about 1metre to get out of deep ruts, or even turn the vehicle in its own length (lotta hard work tho!!) So they are phenomenally versatile recovery & 'get moving' aids! And then with the correct attachments you've also got a powerful clamp, a spreader, a bead breaker, a jack, a brace, AND if you want to make winching in any direction with a Hi-lift easier than it already is with just the basic winch recovery kit & a couple of correctly sized shackles, there's even a kit for that!!
You only need to use your Hi-lift for one really stuck or desperate recovery & it pays you back for lugging it around all the rest of the time when you didn't need it!! If you had an electric winch fitted, you wouldn't pull it off the bull bar just cos you haven't used it yet would you? Or not bother taking a snatch strap & shackles along on a wintertime Hi Country trip just cos you didn't get stuck last time? A Hi-lift jack is extremely versatile as a recovery tool and valuable 'insurance' that can help you in sooo many ways it's not funny! So why wouldn't you take your Hi-lift jack along? After all, it's the single most versatile recovery tool you'll ever own, & even if you don't need to use it too often, it's far better insurance than most of the other crap that people do take along!! They don't take much room & they can be hard work, but they'll keep working and work well when most other stuff has either given up the ghost or wouldn't help anyway!