As others have said, the cost to construct a watch as you describe would either cost several thousand dollars or a few thousand and several months (or years) of work searching for parts. I have not been following the market for the past several years, but I think your best option would be to purchase a good rep with properly-dimensioned (i.e., genuine dimensions) case. Then, replace the crystal, bracelet, crown/tube & dial coronet with gen parts. This will still cost a couple thousand, but you will end up with a very credible-looking/feeling vintage Daytona.
If you want to ice the cake, remove the auto-wind module from the movement (assuming you purchase a rep with an auto-wind movement) and see about locating a flatter caseback, so the watch sits lower on your wrist (1 of the tells of rep 62xx Daytonas is that their casebacks are thicker/taller to accomodate an auto-wind components, which is incorrect for these watches).
p.s. Don't ask me for sources, because I have been out of the hobby for too long and no longer know who is good or in business. It is best to post a request for assistance, so members who are actively buying/building watches can assist you.