Are you sure that "in the same chapel" doesn't simply mean "in the same church" rather than side chapel or other smaller oratory within a church?

No, I'm not sure that it doesn't mean "in the same church". Usually "chapel" would refer to a non-CofE building, and I don't think that applies, either. I think it highly likely that the two girls meant "church", but were gothicising their thoughts again! However, if they really meant a side chapel, then it would not have been at Walcot. It is far more likely that it was at Bath Abbey Church- the central and oldest church in town.

that "saying their prayers" means not a private devotion but attendance at a Sunday morning service of worship (most likely Morning Prayer from the BCP)

I wouldn't bank on it being a Sunday, or it being morning, but yes, I think you are right in it being a public service.

and that such a service would likely be in the nave rather than in some smallish chapel off to the side (at least in a parish church as opposed to a cathedral).

Exactly so. Assuming that the church is old enough to have a Nave, and isn't simply a rectangular building (It wasn't me that called Walcot "a barn"), then everyone would be in the nave and chancel area. Side chapels in churches are extremely rare in this period- they smacked of popery, for one thing, and for another they were contraindicated by the official church policy of everyone worhipping together at one time and place.