What's the current exchange rate on the island?
Whatever it was when you posted the question, it's at least a little different now. Exchange rates vary constantly.
Ummm...., on one purchase, I got a MUCH better deal by having USD compared to a credit card or pesos.
That's extremely unusual. My supposition is that you still overpaid and that the high quoted peso price was to make you think you were getting a great deal in dollars.
By law, prices in Mexico are supposed to be posted in pesos. Anyone (say, souvenir shops) who does otherwise is already violating Mexican consumer law so is a bit suspect to begin with. For example, at Los 5 Soles price tags show dollars but always show a price in pesos as well. If there's no posted price, the seller will quote whatever they think they can get you to pay.
Ummm..., not exactly true. On my purchase, it was $240 USD (cash), and the Pesos amount equaled about $320 (credit card).
Credit charge surcharges are common (and legal) in Mexico, so for almost any honest transaction your best bet is to pay cash in pesos.
I get what you are saying, but I advocate for keeping USD on your person. The amount depends on what you are thinking of buying.
There is really no reason ever to carry foreign currency in Mexico, just as it's practically never useful in the US
I've been to Mexico about 10 times in the past few years so I think it's time to get a Charles Schwabb account. And maybe a Sam's Club membership too.
Sam's Club memberships are significantly less in Mexico, and memberships from any country work anywhere else.
So what is the maximum one can withdraw from an ATM at a time from a bank owned machine?
That depends on a combination of your issuing bank's maximum withdrawal limit and the dispensing bank's per-transaction limit as well as the current exchange rate. At Banamex using my Banamex card, I can get a maximum of MXN$8,000. Using my USAA debit card at the machines in Soriana Mega, I seem to be limited to MXN$6,000 per transaction.