If you were even considering paying cash, Walk into a dealership with $30k in cash and by federal law they would be obligated to report this as a large cash transaction.
I think the limit was recently lowered to $3000. Any transaction above that HAS to be reported
The next thing you might find is the IRS looking up your rear end with a microscope.

All that aside, you have to remember that the dealer makes money on everything not only the sale of the vehicle but also extended warranties, financing, disability insurance, optional add ons, just to name a few
On a credit card on the other hand, they incur a cost of up to 5% that they kick back to the CC companies.
I doubt any dealer would be looking to give away another $1500

American Express rates are among the highest if not the highest at around 5% of course depending on the volume of business a particular vendor does
Consider 5% on 30k that represents and additional $1500 the dealer is not making. I doubt they would want to let that much money go out the door unless you were getting screwed on the front end to make up the difference.
remember there is no free lunch.

Several years ago, I recall Visa (I think it was Visa) that sponsored a GM credit card where you could earn reward points toward a new car purchase.
I would imagine Ford would have the same sort of deal.
I don't know if that still exists
I'm wondering how a dealer would view or perhaps HAVE to view if a potential customer wanting to use a GM/Visa credit card to purchase a new GM product.

I think your best weapon in buying a new vehicle is being informed by using something like Edmunds guide to new car prices (my personal favorite) negotiating your financing rate after you check your bank credit union or whatever and also negotiating extended warranties too, if you want one

BTW, last I heard, you told me you were planning to keep the Edsel did you change your mind? You also mentioned that you found a replacement door for the Yugo, OK so its yellow and the car is green but with a can of Krylon for $3.99 you can make it look real good (You might ask John as he will lyk if it's on sale at wal-mart or where to get it for less) you should be ok.
Oh, and I did want to mention the turbo decals you put on the hood look really cool.

If you do go that route, please lmk and I'll send you that pair of fuzzy dice for your rear view mirror and the dog with the bobbing head you always wanted for your package shelf.
It would almost be like having a new car