Last summer I did some spread sheets on building up a bike. I think the answer is its tough to call and its only reall cheaper to go down the doner bike route if you find an amazing deal and your really going to use every thing.
If you start swapping stem, seat post and replacing cables it eats into the advantage
But buying a lightly used women's specific bike would be the cheapest option it won't loose much value if you need to re sell it and it'll save alot of farting around.
I'll venture an opnion that's not been asked and is probably unwanted.
Either buy yourself another bike or buy one for Mrs Trout. I don't think either project will benefit from trying to be the other……