Another way of saying D aeolian is to say that the song is in the key of B minor which fits much better. I always used to try and convert minor songs back into their major equivalents too, but its easier just to learn songs as minor songs when that's what they are, less mental gymnastics if you know what I mean
Pretty much playing B minor scale over this whole tune will work in almost all cases.
Two exceptions I see are the F# as you noted and the E major chord which diatonically should be minor. In the F# chord, the scale changes to B harmonic minor which gives F# chord a dominant quality and is done all over the place when the V chord is involved. It happens in Blue Bossa for example, changing C minor scale to C harmonic minor for the V chord, (G7), and back to natural minor the rest of the tune. Otherwise, the V chord would have been G min7 and that just wouldn't work in the tune. I guess you just don't want to have a minor quality in a V chord as it really kills the tension and release of the V I cadence.
As for the E major or E dominant chord, well, poetic license? Actually, I think thats the use of a secondary dominant. Basically, any diatonic chord in a key can be changed to a dominant chord and that happens a lot too. I wish everything was diatonic sometimes, makes life a lot easier, but not quite as interesting.
This is a brilliant tune. I notice that it walks down the B minor scale in pairs of I-V cells, moving from the I to its V (Bmin-F#7), then to the bVII to its V (A-E), then to the bVI and its V (G-D), then a IV-V (Emin-F#7) turnaround back to the I chord (Bmin), always using major or dominant chords in the V's for the tension release factor, and that's why they used E as a secondary dominant in that descending sequence of otherwise diatonic chords. They change Emin to E for the tension and sense of movement it brings.
A long winded answer I suppose and of course, I could be totally wrong, but I don't think so. Thanks for bringing up this great question, I love doing the harmonic analysis.