Running an AD&D adventure ("The Ghost of Harrow Hill") in 5e; any advice?

[Thane of Fife]

The final boss is a monster that didn't make it past 3e, so I'm just using a Deathlock, but I'm not sure if I'm missing something. The villain of the adventure's the ghost of a wizard, and the final battle is him forced into his decaying former body. The original adventure basically makes him a melee only undead, and I'm wondering if that was the point, and I'm losing something by using a spellcaster undead.

Spellcasting undead are mostly just not a thing in AD&D (except liches). The fear thing is supposed to be a ghost thing, not a spell. So it's mostly just a matter of taste on your part if you think he should have spells.

I'm a little worried about treasure too, since AD&D hands out +2 and +3 weapons like candy. I was thinking of just nerfing the +2 and higher weapons down to +1, or replacing them with uncommon magic weapons, but I'm not sure that's the best approach?

It doesn't look like there are that many magic weapons in that adventure, and only one is a +2 weapon, so I'm not sure what you mean by handing them out like candy (the adventure does try to ensure the PCs will have some so that they can fight the ju-ju zombie, which is immune to nonmagic weapons). But generally, I would say that the adventure tries to stick with low plus weapons so that the PCs can't fight the ghost, while including that one +2 as a hail mary.

Implicitly; he only has a very basic fear spell on his ghost statblock, but he shows up throughout the adventure to do scary house things™ (like summon enemies or seal up houses).

I think that's supposed to be just generally spooky stuff, not magic. I think the adventure actually originated as a Ravenloft introduction, and those are supposed to be like little darklord abilities.

I think what I might do is just roll a random treasure hoard and distribute that (aside from one specific case of a Luck Stone that feels very thematically appropriate). Should be way easier than trying to make a judgement call on how many of the items are too many.

Having run this adventure in 3e, I'll note that it's pretty generous with healing items, because the PCs are trapped in the house and can't get out to rest. You may not need those in 5e, but it's something to consider.

However, what would be the reason to force the ghost back in the corpse, if not to cut out the access to magic? Just not having to deal with ghostly abilities?

The premise of the adventure is that the ghost is just way too powerful to fight, but it doesn't really attack until midnight, so the PCs have to figure it out before then. The "ghost abilities" are basically scripted attacks it makes before that.

Personally I would make the Ghost Wizard an illusionist or enchanter,

I don't think that the adventure makes much sense with the wizard being anything but a necromancer.

About the grabbing hands: are they Crawling Claws? Because those are in 5e.

The hands don't move. They just burst out of the floor, then try to grab someone and drag them under (to instant death).