This is great information -- thanks so much cws. Going landside was just a bit of a lark, given that at least we know what to expect with the heathrow express because we've done it. T5 sounds as though it will be easy once we get there, and so long as there are lifts in appropriate places in T3, the fact that the distances are long is not a problem.
As for why no direct connection at T5, it's all about the taxes on BA awards. While we would prefer BA going transatlantic for many reasons, not the least of which is a T5 connection, unfortunately, for a family, the taxes really do become nearly prohibitive and the fees and taxes on AA transatlantic comes out about 1/5th the price.