I finished the game with 2,912,699 XP; for level 71 you need 2,943,000, just a 30,301 XP difference.
I had 8 suppression battles, the initial single assassin battle, 7 heroes and 8 bosses; total of 24 battles. Klissan spawned 4 AK scrolls and another shop sold 1 AK, so 5 AKs total good for 25 battles. Note that the only battle that I fought without an AK scroll on was the initial single assassin battle. Also note that there is no dragon digging chests in this campaign.
I took paladin to fast-track level 3 Learning, and also had 2 Hand of Necropolis spawn, one at the guild with contracts (so I was able to buy that one at once) and one at the undead (veteran's guild) lands. This one I wasn't able to get at once since dieing was not an option (it is like subtracting half a level worth of final score points); this also means no black knights/bone dragons since you only get the high tier undead units if you die.
Suppression of level 4-5 items would give 12k-25k of XP (this estimate is already with AK/Learning 3/HoN), so given the exact same setup as above PLUS 2-3 more level 4-5 item suppression battles then level 71 IS possible.
This is a rare setup to generate:
1) 5 AK scrolls (most of which should be sold by Klissan)
2) 10+ suppression battles, most of which should be high-level items
3) 2 Hand of Necropolis, one of which should be accessible almost immediately
Good luck to all!