That's not quite how it's used, Anon.
Use "whomever" where it can be replaced by "the person whom".
Use "whoever" where it can be replaced by "the person who".
Thus in your examples:
1. Either Mark, Jill, or Sam will be coming for this package; you will give it to whomever arrives.
— No; "you will give it to the person who arrives"; thus whoever.
2. You will give this package to whoever comes to the door.
— Yes; "you will give this to the person who comes to the door; thus whoever.
3. I'll go with whoever wishes to come with me.
— Yes; "I'll go with the person who wishes to come with me"; thus whoever.
4. I'll go with whomever wishes to come with me.
— No; "I'll go with the person who wishes to come with me"; thus whoever.
Cf.
5. We will be happy with whoever the voters select as President.
— "we will be happy with the person whom the voters select as President"; thus whomever.
All the best,
MrP