Yes May-June time is the low season fro Los, and usually when I travel there, China air is the cheapest airline flying there, but as you say long stopover and who wants to go all the way to Beijing? Looking at your dates Turkish is £408 with not bad stopover in Istanbul, I'm all for saving a few quid, but sometimes prefer to pay few quid more to save the long journey, for example this May I went with EVA for about £460, direct under 12 hrs, year before a cheap flight with KLM, quick hop to Amsterdam, and short wait then straight off direct to Bkk, had a few bevvies from two female slovak basketball players, woke up with couple hours to landing.