It shouldn't be too difficult to get it right for Jane Austen's period. There were a not insignificant number of publications and manuscripts containing popular dance tunes. I often come across references to these in notes in tune books. The instrumentation should not be too difficult, either. Violin, woodwind - flute and oboe mostly, (clarinet less likely at that period) plus either cello or serpent for the bass. Reproductions of late 18th cent/early 19th century instruments are available from modern makers.

A group such as the Mellstock Band would almost certainly be able to supply suitable music on appropriate instruments.

What is really needed is a sufficient desire to get it right - at least within the limits of the budget - and I suspect that is what is lacking. Earlier adaptations of Jane Austen by the BBC were usually reasonably OK on the music with suitable instruments and tunes from the Dancing Master. That particular publication would have been long out of date by then, but many of the tunes would still have been in circulation.