This sounds like you need a Many to Many relationship.
One project has many customers.
But also 1 Contact is used on Many Projects.
So you need to make a new table called Project Contacts. Then make two relationships.
1 Project has many Project Contacts
1 Contact has Many Project Contacts.
When you get that working, you will want to edit the field for related contact on the new table so that so that once a lookup field populated for the Company on that join table, that the drop down list only lists Contacts for that same company.
Once you get the many ot many set up, I can help you improve that drop down list if you get stuck there.
