That is, I would like to stay in Turkey for 180 days. Is it possible to do this by first applying and getting the eVisa 90 days before my arrival in Turkey so the duration of my stay lasts through the second half of the 180 day window. Next, after those 90 days, I would leave the country for a day and get another eVisa, then enter the country again for another 90 days. This would essentially let me stay in Turkey for about 180 days. Is there some flaw in this plan?
Is there some flaw in this plan?
Yes. They might not give you the second visa. And, even if they give you the visa, they might not let you in.
I don't know about Turkey but some countries aren't happy about people chaining together visitor visas to spend a longer period in the country than a visa normally allows. It's safest to get a visa that allows you to stay for the time you want to stay. If no such visa exists, then you must be prepared for the possibility that you won't be able to make the visit you want.