Can I stay in Thailand for up to 6 months with a MEV, and how do I handle my ongoing flight?

Now let's address your first question

𝗜𝘀 𝗶𝘁 𝗰𝗼𝗿𝗿𝗲𝗰𝘁 𝘁𝗵𝗮𝘁 𝗶𝗳 𝗜 𝗵𝗮𝘃𝗲 𝗮 𝗠𝗘𝗩 𝗜 𝗰𝗮𝗻 𝘀𝘁𝗮𝘆 𝘂𝗽𝘁𝗼 𝟲 𝗺𝗼𝗻𝘁𝗵𝘀 𝗺𝗮𝘅𝗶𝗺𝘂𝗺 𝘄𝗶𝘁𝗵 𝗯𝗼𝗿𝗱𝗲𝗿 𝗿𝘂𝗻𝘀 𝗮𝗻𝗱 𝗲𝘅𝘁𝗲𝗻𝘀𝗶𝗼𝗻𝘀 𝘄𝗶𝘁𝗵 𝗶𝗺𝗺𝗶𝗴𝗿𝗮𝘁𝗶𝗼𝗻?

Actually you can get almost 9 full months of stay out of a 6 month METV if you work the bounces right AND you get the visa as close to you entering thailand as you can (because the 6 month validity starts running down from the date it's issued)

With bouncing every 60 days it goes like this;

get the visa

ENTER thailand get 60 days

when that 60 days is up, exit/re-enter to get another 60 days

when that 60 days is up, exit/re-enter to get another 60 days

when the VISA is almost going to expire, exit/re-enter to get a final 60 days taking you to about 240 days and get the one 30 day extension on that you're allowed at the immigration office for 1900baht taking you to 270 days or almost 9 months.

You can cut one bounce out of the above scenario IF you get a 30 day extension on each entry BUT you still need to bounce just before the VISA itself expires to get that final 60 days so you can extend it by 30 more and get to 270.