Just to add to the soup, you could also consider the Yamaha TDM. It's worth a look IMO. Great value as a second hand buy and seems to be tough enough to take what you want to throw at it.

After that, well there are loads of opinions in here about the whole range of bikes that you have already identified (a lot of it is in the technical bike forums as well as in this forum) and the factors that you have listed.
So, at the end of the day, you will go with whichever bike you are most comfortable with no matter what anyone else says!!

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Dave

Sounds like you need a fuel injected bike to cope with altitude changes and screw & locknut tappets for valve adjustment.

DR600 - getting on a bit now, kickstart only - no good if you've dropped it & hurt yourself. Get a DR650 with e-start if you insist on having one. Aqualine do large tanks as do several others.

Old XT's - old, getting a good one will get harder the longer you leave it.

Africa Twin - take a spare fuel pump, bit heavy for the power?

Chains need not be difficult if you fit quality kit & look after it.

Rebuilding an old bike - not necessarily cheaper, you may end up finding yourself needing to replace more parts than you first thought, always works out more expensive than expected. Then there's the labour cost if not doing it yourself. Best bet is a low mileage bike in good nick, check it over, fit new consumables (pads, chain, sprockets etc) & take spares.

Shaft drive adds weight but in the case of BMW's, some of that is offset by the low Cof G due to the engine layout. With 1150's, the torque available low down the rev range makes it easy to ride offroad at a moderate pace.

KLE500 lacks torque IMO, not good when fully loaded although I believe they're easy to service?

KLR650 is not a DR600/650, very different. Dull but apparently reliable if the Doohickey mod is done, popular in the US where big tank versions are still available.

Some single cylinder bikes may be harder to service than a twin, it's not a matter of counting the cylinders to calculate the servicing needs. The GS range all have screw & locknut tappets whilst KLR's use shims but in an ideal world, they'd need adjusting less frequently - it's case of balancing the servicing needs against your spannering abilities. Less skill, get a simple to service bike even if it needs servicing more freqently.

Regardless of what you choose, when it comes to servicing, it's not just a case of following the Haynes manual & all will be well. You need to have certain amount of empathy with the bike, an understanding of how various components interact with each other i.e. the need for correct chain tension on a loaded bike and the possibility of wrecking a gearbox if you run the chain too tight.

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