Join Date: Feb 1999
Location: San Jose, California, USA
Programs: AS 100K, UA MM, AA MM, IC Plat Amb, Marriott Gold, Hilton Gold, Hyatt Explorist
Posts: 3,146
In general, I recommend making new reservations before cancelling the existing ones, so your approach makes perfect sense -- it's just that in this particular case, it doesn't work due to AA's (understandably) aggressive policies and procedures to combat speculative bookings.
Because you booked the original flight via an OTA, it would be better to have the same OTA do the rebooking, if at all possible. The OTA can do it as an effectively atomic transaction (that is, cancel the old itinerary and rebook the new one at a confirmed price) so you don't have to take the risk.