I don't think date-of-ticketing makes a difference with the new same-day policy. I think it went into effect globally for everyone on June 17th.

However, my very recent experience with changing reward tickets as a Plat is that as long as reward inventory is available and it's the same routing, e-tickets can be changed to any alternate date with no fees whatsoever. There may be fees or other restrictions on this for non-Elite travelers. The same-day stand-by rules do not apply; they just re-ticket you. I've done this on both outbounds and on returns with rewards, changing to completely different days/times provided that 'Saver' inventory is available - and probably they'd do it for the additional miles if only 'EasyPass' was available. I recently changed HNL -> JFK to the next day's HNL -> LGA (change was made the morning of the original flight), though I had to go through the Internet Help Desk; for some reason, the regular Elite call center couldn't ticket the flights that I could see doing a search on co.com.

I have no idea how it might work with paper tickets, however - that could be the showstopper in this case, unless your new flights are far enough out that new paper tickets can be issued via a call to the service center. I'm guessing that the airport ticket agents will not be able to help with changing anything on a reward ticket, eletronic or paper.