I noticed you’ve been through some of this in another question already as well, and it’s not simple! Unfortunately we can’t give personal advice and recommend specific credit cards here, but this is my take on how I would research this.
I think the only way to do this is to spreadsheet it. But first you need to gather some data…
How much do you spend on Amex? What are the surcharges to do so?
How much do you spend on Visa/MC? Again, surcharges?
You will then have a $$ figure of the total cost of paying by credit card.
Then you can sift through the Cards Table here. It’s primarily American Express issued cards (i.e. not bank issued Amex) that limit earn on government transactions, and even though some other banks have a government clause it generally refers to ATO spend.
Find some which would work for your taste for annual fees / other benefits you’d be looking for and chuck their points earn rates and fees as options to consider into the sheet.
You can then work out how many points you’ll earn, and the cost of earning them (surcharges plus annual fees).
If you know how much you value your points at then you can figure out which cards are greater than that point value.