Or, reason backwards from a 1DX III.
So $6,499 less the features the 1DX III has and the R3 doesn't have, which would be what exactly? Oh, wait, the R3 has the $650 WFT-E9A built in, it also has more fps and more mp. So $6,499 plus $650 plus 10% for being 'better' = $7,864.
Now that was slightly tongue in cheek, and Canon have said the R3 sits between the R5 and the 1DX III in the model range, which would imply the price should be somewhere between $3,899 and $6,499. Of course your guesses are between those numbers, but as all R bodies have carried a premium I wouldn't be surprised to see the release price of the R3 at $5,999, and at that price I believe they would sell every one of them. I do not see an R1 coming out at $6,499.