Crowman...Obviously you've put some thought in to the question of whether In the Beechwoods could be also a Barrett solo track under another title. My initial thought was, before examining the Milky Way similarity, also that Swan Lee would fit into the Beechwoods track quite well. Especially noting the similarity of verse parts in the finished Swan Lee. There are some very strong similarities in the beginning of each verse, the two seem to fit pretty well, but then become very different....
However, I love the idea of a bouncy English 60's psych tune about Native Americans and the wild, it would have a complete strangeness about it, and would make sense that Syd got to add his sax and banjo to the tune in a solo effort, assuming hypothetically that Beechwoods is the track he had in mind for those instruments....you know, the story of Barrett's desire for sax, backup singers, banjo? which was scoffed at by the others. The thought is very tantalizing, a free jazz piano and sax solo in the middle of an english pop tale similar to John Smith and Pocahontas with grand organ and ripping guitar and old fashion banjo to boot. High wierdness.
The Syd backing track Silas Lang, which is buried in the final Swan lee ,with the sax and banjo has some tricky differences from the Beechwoods track..the intro and outro, are hinted at in Beechwoods with the long organ notes, but when compared to how the outro of Silas Lang is buried in the final Swan Lee track some questions arise about how the lyrics of Swan Lee would even fit in Beechwoods...too many stanzas if I recollect and the chorus does'nt fit at all, unless it were repeated more times in the Beechwoods version, but then the song length would have to change dramatically and changing the tempo throws everything off. I had trouble getting them to fit without pretty major structural changes..including lyric changes. All that being said, they could still be very different versions of the same song.
You are right that the key/chords are different in Milky Way and Beechwoods, but rythmically the two songs are nearly identical and equally as similar in exactness of duration and lyric placement. It is difficult for me to think of that as coincidence. I cannot be 100% cetain that they are the same song, but I find it likely, at least structurally and also Barrett recorded his Milky Way towards the end of the Barrett album on the same day as he attempted Millionaire(she was a Millionaire)an old Floyd tune. Which would fit the logic that he was attempting to record old songs as he was running out of new ones. songs he had'nt gotten a chance to release with Pink Floyd.
I can't imagine why a perfectly fine take of Milky Way in 1970 would not have been worked up further and included on the Barrett LP. I guess there could be many reasons, but maybe one reason being that it would create legal problems, also being a Pink Floyd tune. The same goes for Opel on Madcap, which is another song that I cannot understand not being released at the time it was recorded. When scraping together a record of scrappy tunes that are being filled out with other's arrangements, why leave off these two excellent songs. Bob Dylan Blues being left off makes sense, the guys did'nt want Syd in trouble over what could be percieved by some as an attack on Dylan. Perhaps I'm just a loon. It would be nice to have some of these questions answered by the parties involved. Simple clarification of song titles would resolve a lot of this speculation.