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“...Any other suggestions would be much appreciated...”

Well, others probably will disagree, but I ground my suggestion with your words: “i am now fixated on visiting this area for some reason”, “Vilnius, which to me sounds like the most interesting city”.
1. Tallinn is the nicest (“nicest” is not the same as “most interesting”) and the smallest at the same time. Old Town is doable within few hours with out any rush. So 1st day “explore Tallinn”, and next day drive to Saaremaa as early as possible. If it was me I probably would try to leave Tallinn same day, arrive in Saaremaa in the evening, not to worry if it will be late evening or night. At least i'd like to wake up “at the spot”.
2. Don't know why you want to spend there (in Saaremaa) all full day, but ok, spend all day and drive to Riga next morning. One could drive same day in the evening and arrive to Riga at the beginning of the night, but since you'll be traveling (i.e. you are not on business trip) you don't need to get from the point A to the point B as fast as possible: quite opposite, your “getting from the point A to the point B” should be meaningful and should count as an exploration. So the road between EE/LV border to Riga goes along the coast, you can see the sea here and there, there are several spots for the short stops, etc. This section of your trip can be quite meaningful.
3. Direct transfer from Riga to Vilnius means that the time is wasted for the transfer only. The road is boring and does not tell about the countries anything. This is not bad, but should be taken into account.
4. Curonian Spit in late September is completely different thing in comparison to the summer time. Summer ends up on 31st of August. In fact even now one can feel the scent of the autumn, the summer is almost over, the trees and grass are still green, but it may change very quickly and at any moment, starting from September 1st. So if you was reading something about the Curonian Spit, if you saw some images – it was probably from the summer time. In late September you won't find anything what you have read, and the scenery will be quite different, plus add the strong and freezing wind. It's not bad, but i'm local and know what to expect. If you have some certain expectations based on the reports from the summer time you may be very disappointed. Or surprised.
5. On the route from Riga to lithuanian coast there are several “objects of interest”, namely Kuldiga town (a “capital” of Curland), Karosta prison in Liepaja for those who are obsessed with soviet “horrors” or Samogitian National Park for those who are interested in natural enviroment with some history and the “scent of pagan times”. Those “objects of interest” are exactly on the route, other objects involves significant detour (“significant” for you because your time is extremely tight). And if you want to drive the fastest and shortest route from Riga to Klaipėda – drive Riga-Saldus(LV), turn south to Mažeikiai (LT), drive straight to Plungė, cross the road Šiauliai-Palanga No A11 and drive on thru Plungė on to Vėžaičiai, then enter the road No A1 and drive up to Klaipėda. There are no “objects of interest” on this route. Western travelers who are traveling by bus go other route which is longer.
6. Entering Curonian spit involves a transfer by ferry. Takes ~15 minutes. Should be no lines. However the speed on the spit is limited, and there are restrictions for cars: you can't stop or drive anywhere where you want.
On the way back from Curonian spit there should not be lines (waiting for the ferry) either. You cross the town of Klaipėda in some 10 mins (including the time you have to wait at the traffic lights and excluding any possible traffic jams). So, the driving from Jakai roundabout at the outskirts of Klaipėda to Vilnius boundary will take 3.5 hrs non stop and if you don't violate the traffic rules. If you overspeed you can save some 20 minutes, but you will lose about the same if you'll be stopped by cops.
At the Vilnius outskirts may be some traffic jams: there is a serious reconstruction of the bypass and the main crossroad, it will take probably some 2 years until it will be completed. So this is regarding how much time it may take.