Having experience with those breeds myself, I believe it sounds like a good plan. However, how are your Cornish laying? I had Dark Cornish and didn't get as near as many eggs from them as I did our Delawares and New Hampshires, which both were/are good, steady layers in my experience. However, half of my Dark Cornish birds got a bad start and I think that a bad start can affect egg laying throughout the life of the bird, so maybe my Dark Cornish were poor layers without it being a breed trait. But for me, I'd be doing a bit of back crossing to keep up egg numbers (which I think is what you say you're going to do) while still trying to retain the broadness of the Cornish.
Oh, and what do you think ... do you think what chickens are fed has much bearing on their taste or do you think it is all in the breed/strain? To me, what we feed the chickens makes their eggs taste better.
Good luck! Post photos sometime if you get a chance.