'Say to' is not a normal quotative verb, and so its use as one is at best dubious (though the rules do seem to be relaxing in this area).
From the Britannica Dictionary:
Ask the Editor
Using "Said" with Direct and Indirect Speech
When converting indirect speech into direct speech, when should we use
said and said to?
Answer
When you are repeating the exact words someone spoke, that is direct
speech. Use said with quotation marks, as in the examples below:
- She said, "Go home!"
- He said, "Stop working at 5:00."
- Mark said, "Turn left on the next street." I said, "I'll be home later." ...
When you are reporting what someone said, but may not be using their
exact words, that is indirect speech. Use said to when reporting a
command. Use said that or said when reporting information that was
given. Do not use quotation marks for indirect speech, as in the
examples below:
- She said to go home. [said to because "go home" is a command]
- He said to stop working at 5:00.
- Mark said to turn left on Main Street, which is the next street.
- I said (that) I'd be home later. [said (that) because "I'll be home later" is information]
- My mother said (that) I was going to be late.
- The children all said (that) they were hungry.
You can switch to an accepted quotative verb:
- He demanded "Take [him] to the store right this second"
But this doesn't sound as natural as the obvious quote, and could be confusing. I'm not sure I could ever see an advantage in switching pronouns in this way.
The corresponding report structure:
- He demanded/asked that we [should] take him to the store right that second
is unremarkable, fine.