It would be possible, and neat, but they'd have to do the following things:

-greatly reduce max enemy HP all around, especially for NM/HNM. Possibly other enemy nerfs as well

-introduce a FFXII gambit-type system, allowing macros for 5 other party members. I don't think 18 would be realistic (which is one of the reasons why they'd have to drop NM HP drastically). Alternatively, so it won't be overwhelming, allow only 3 party members like FFXII, and nerf monsters even more

-as a possible addendum to that, maybe introduce a mercenary guild to replace the LFP system. Kinda like Tactics, you go to the guild and hire specific jobs. Levels, AI, and gear may even vary. You can check them in advance and get what you pay for.

-reduce the cap on all crafts, making it possible to get 100 in every craft

-Eliminate many of the intended gil sinks, such as chocobo rental or NPC storage

-of course eliminate the AH, unless they wanted to randomly generate stuff on it for you to buy

-To coincide with that, all NPC prices would have to drop. More items/gear would need to be available through NPC, and quests would need to offer much more gil rewards. Possible large increase on the gil that beastmen drop as well

-drop rates would need to increase significantly, since there is less supply. Also it would expedite some missions and quests, allowing you to full appreciate the story more

-less xp required for level up. Maybe even increase the level cap to 99, making some HNM easier to defeat since you won't have an alliance+

-Either introduce Mog tents, or provide more places in the field that restore HP/MP (ie save points). Resting like you do in the online version would really suck. Reduced NPC prices on meds would help to this end too

Overall, I think it would be cool, because FFXI has a pretty good story. Its just hard to get a grasp on it at times and comprehend it, because you'll often find a large lapse between cut scenes due to the grinding nature of the game.

I don't think you'd have to change the story much at all, because it would be like FFI with no pre-fabricated character as the main hero.