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Join Date: Jul 2002
Location: MCI
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Actually, I wouldn't completely rule out Southwest.
It looks like LED-JFK actually has competitive one-way fares. (Aeroflot around $300 one-way.) So pairing a one-way with a WN nonstop LGA-MSY (around $100-150 most days in November) could be an option. <Insert all the usual cautions of using multi-itins here.>
That said, it looks like there are tons of cheap LED-MSY round-trips available for those off-peak dates. OP is probably best off just taking a stab at his likely return date and buying an R/T on the carrier with the least-bad change fees. The only issue he'd likely run into with fare bases is if he tries to change to a peak date around Mardi Gras.
I do multi-itin once or twice a year, and often adding an overnight in New York to do it, but usually it's because I have 4-6 people traveling and the cost savings are at least a couple hundred dollars per ticket.