You are correct in that Reg. E doesn't allow you to require a written notice and that you must begin your investigation when you get the oral notice. Your clock starts at that time for Reg. E anyway.
I don't know that Visa allows your clock to start only AFTER you get a written notice. If it does, you're following those rules. If it doesn't, you need to follow the zero liability rules and the 5 day provisional credit rules Visa imposes and which you contracted for.
If you apply the Reg. E liability and then, properly following the Visa rules, determine that zero liability was applicable, a recrediting would be required. If the Visa rules do not allow you to require a written notice (forget about vendor requirements with your investigation vendor, focus on your agreement with Visa and with your customer) then you need to follow all the rules from the time of the notice, i.e. zero liability and 5-day provisional, when it is through their network.
My opinions are not necessarily my employers.
Rules and Regs minus Relationships equals Resentment and Rebellion. John Maxwell