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

[Unoriginal]

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).

Could be nice to replicate that "ghost with magic, corpse without" formula but making it explicit and more obvious, I think. Or you can go spellcaster all the way as you planned.

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?

Personally I would make the Ghost Wizard an illusionist or enchanter, using their spells to fool and manipulate anyone in his area of activity very efficiently while taking advantage of the ghost abilities to remove the weaknesses such a caster usually has. Meanwhile the Corpse Wizard don't have magic and can't just disappear to keep messing with the PCs, but he'd be an ultra-aggressive juggernaugt, like a Slasher villain with a grudge-fueled determination to pummel the PCs into next week and keep hitting.

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.

Can be a great solution, indeed.

Aside from the final boss (and some grabbing hand things that I'll probably just make a complex trap), they're all creatures that made it (undead are persistent like that ;) ).

Undead are persistent, but their power levels vary widely from edition to edition. That's something to be careful about.

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