I don't think a bigger bodied, longish scale instrument is necessarily the way to go, as Hamish suggests. When I play fingerstyle melodies and accompaniments along with the concertina on my larger instruments (a Froggy Bottom F, Bourgeois D and a Lowden F[cedar top]) I tend to get to get drowned out, although these instruments sound great behind it when strummed. I've been going down in size using an OM and now the Collings OO. The smaller body instruments just seem to cut through better in this situation.
Of course, I'm working with a concertina and have no experience with a melodeon so I'm not sure how the two compare. It might be a good idea to take the melodeonist along to play with when trying out instruments, if possible. Good luck. vl