On the following site (if the long url works), look at examples 7, 8, and 9:
The ebay flutina arrived and though the bellows were in good condition as described I could see that this instrument was going to need some work in order to be played. It was the early single row version, with no chords on the left hand, just a finger operated air valve. This model had small keys, I suppose made from M.O.P, a bit different from some of the ones I've seen in pics which look like large flat mother of pearl pieces and are often missing from ones I've seen for sale. It had the two drone valves on the right hand side operated by a pretty crude mechanism fabricated from brass sheet and it was difficult to figure out what would supply the pressure to keep them closed. One of these drone notes seemed badly out of tune when I tested it. All of the other notes played, in varying degrees of tune, but there was a lot of leaking air. I decided to take it to an accodeon specialist in Philadelphia, about an hour away, and spent about an hour discussing it. In order to return it to playability he would have to part off the bellows, as on this early construction there is no way to open the instrument up as on later styles. Had I wanted to proceed he would have replaced the leather pads that seal each note, and repaired / replaced / restored the internal leather valves as needed. While he was testing the operation, playing scales, I asked him to note what key it was in - it was close to "g". As is frequently the case, this particular instrument would have cost more in restoration money than what I have into it and so I've reluctantly decided to return it for a refund, which was part of purchase terms.
As Dick mentioned these typically had only one reed per note and with the small size of the bellows (just four folds) and I don't think it would ever have been very loud. And no, I surely wouldn't have made the faux pax of playing this in accompaniment with the fiddle; Renny, our fiddle player also plays banjo. I am though planning on featuring two banjos in the band on certain songs.
I mentioned to Mike, at Liberty Bellows, that there was a huge interest in these early accordeons amongst the early banjo community and would it be feasible to make new reproductions. He supposed that it would not be a difficult instrument to reproduce and that getting the correct size bellows made up would probably be the most expensive part. As I could see he seemed a little interested in this idea I had to admit that "huge" was probably not accurate, that there might be a demand for maybe a dozen or so. Thus ended my dreams of adding the sound of the flutina to the Camptown Shakers. While I was there I also had him look over the 10 button, circa 1920's, accordeon I have been playing on and decided to put a little money into giving it a routine servicing. He remarked that it was nice instrument, if a bit on the small side (child's?) and I'm sure I won't be able to resist using a bit with the band as I'm kinda hooked on the reed - banjo combination. I should have just stuck with the harmonica.
I don't think they have ever worked on anything this old before, but Mike seemed willing to work on anything and I saw them doing pretty extensive work on a few later accordions on the bench. Knowing that a lot of the flutinas for sale need bellows work I asked him if replacements could be made up and he said that yes they made by a bellows specialst but that this is pretty expensive. The way that works is that the bellows are removed, and sent to the specialist who makes a new one to the pattern of the original. Before closing I should also mention that Liberty Bellows has on consignment a very old concertina, supposed to be Civil War vintage. Mike mentioned that when the seller brought it in he had an image of the original owner (ancestor of seller?) in uniform with the flutina . This was a very large instrument, very beautiful with detailed marquetry covering all of the surfaces. At around two grand, it was out of my consideration, but worth investigating if anyone was interested. I don't think it was on their web page inventory yet. He also had a similar vintage concertina, with a more plain appearance for about half of that. My personal experience with accordeons is with the smallish one I've had and I hadn't realized how large these concertina were.
He makes this salient point: "The accordion, when used, seems always to have been a substitute for the violin, rather than an addition to it."
So, I just mention it. Heaven forfend that the Camptown Shakers (or somebody else) should slip up and put the fiddle and accordion onstage at the same time.
Once again, making assumptions can be dangerous. I just came across this sheet music cover of White's Serenaders. Look at the guy to the right of the fiddler.
I have a 22 button Lachenal Anglo (probably 1870-ish)- It's got the accidentals you describe, but is actually pretty awkward to play in D due to the location of those buttons. My gut feeling (after playing around on single row accordions and anglo concertinas for 35 years) is that most (non-virtuosic) players would have happily played along on the G tunes and refilled their drinks when the action moved to D. As you say though, there are lots of D tunes where you can cheat around the C# - especially if others are playing the tune too. I do that all the time. In Canada (especially Quebec) there are lots of accordion versions of fiddle tunes that do this, except now it's usually a matter of playing in A or G on a D accordion.