Playing the episodes earlier is a no brainer. However there was a lot of interference IIRC by FOX on the making on the show beyond just the order of the episodes, marketing, script rewrites. Basically they wanted to turn Firefly into a "pure" action comedy.
A good POD might be for Whedon to have a falling out with FOX due to their overt interference with Firefly. Let's say he refuses to rewrite the pilot or something. Firefly doesn't get picked up immediately in 2002. Whedon doesn't give up on Firefly however and soon enough there's a need for mid-season replacements.
UPN is the most likely target here. They are severely lacking in good shows and already have another Whedon show
Buffy playing on Tuesday nights. In OTL
Buffy was followed by a number of shows that got poor ratings and lost a lot of the former's viewers. In TTL Firefly is an unknown quality (not the abject disaster it was in OTL due to Fox's interference) and another Whedon show. UPN therefore picks it up for a temporary run of 10 episodes and it is scheduled to replace
Haunted at running from 9-10 on Tuesday evenings.
TTL's Firefly is much better marketed and it is hoped that it can be a successor to
Buffy. It's arrival on the scene in January 2003 sees it not only maintain Buffy's viewership but actually increase slightly. The first 2 part episode manages to gain a considerable number of viewers as it is shown twice. Firefly's numbers remain strong for the first half of it's 10 episode run at around 4 million viewers (not impossible given the competition). It quickly earns rave reviews and is renewed given enough episodes to fill out the 2002- 2003 season and a full slate of episodes in the 2003-2004 season.
The success of Firefly makes UPN reconsider it's Tuesday lineup, instead of switching to sitcoms, it remains a "Whedon night" as a Buffy spin off is picked up to replace Buffy in the timeslot preceding Firefly. Again Firefly does well enough and actually manages to pick up steam attracting a fairly large following. The success of Firefly prompts UPN to maintain it in their lineup until the network's dissolution in 2006.
Following the collapse of UPN (let's face it even a vamped up Firefly won't save the network) Firefly is shopped around to different networks including Sci-fi, who opts to pick it up for it's final 3 seasons (Whedon originally planned 7 seasons IIRC).
At the end of season 7 in 2009 all of Firefly's plot threads are tied up and the series comes to a conclusion much to the joy of sci-fi fans everywhere.
BTW a great resource for any TV AH:
http://en.wikipedia.org/wiki/List_of_United_States_network_television_schedules