I did the same trip last winter and flew into GYN then went to TBS and then to EVN - this was the best / cheapest way for my flights from Europe, as well as the flights between the cities. I recall I could only book the Georgian Airways TBS-EVN flight around 3 months before travelling.
I would also agree with Georgia being the place to spend the most time - a very welcome and navigable middle ground between the nouveau riche GYN and the rather Sovietish EVN.
My understanding was that there could only an issue doing GYD after EVN if you visit Nagorno Karabakh first.