Rowan: what you describe sounds like a harmoniflute. It's built like a flutina, but has a three-octave piano keyboard (I think some may have been four-octave). It's played exactly as you describe, and is often called a lap organ. There seems to have been a stand available as an optional extra, with a single pedal which somehow connected to the bellows, thus enabling it to be played with both hands. I wonder if this is the instrument as described by Sian above. If you google 'harmoniflute', there are some photos of the instrument - both with and without these stands - in museums. Tne Indian harmonium certainly is supposed to have developed from instruments introduced by missionaries. I gather the impression from your email that you are in Oz. In which case, you might be interested to know that the one I have (bought on ebay a few weeks ago) has the name and address inside of somebody in Oz, who I take to be its original owner, and the date 1857. The instrument is not in the same place as the computer, but I'll open it up when I get back there and check the details and get back to you. You never know - It might be your great-great-grandad!
Just returning to Dick Miles' original questio: 'Do people like them'; I think you can see from the number of posts here that they certainly arouse plenty of interest, and my own experience of using the instrument - in groups in the past, and now as my main accompaniment as a solo singer, that people do like it. It always arouses interest, and people always come up to me afterwards to say how much they enjoyed listening to it. Many people make the comment that it sounds good accompanying the voice, and they like hearting songs played on it which they have previously heard on guitar. In fact, a regular comment is: "where do you get them? - I want one!".
John Kelly.