McPete, you have confused me a bit. You started off saying that the roadie would be the workhorse and the tourer would be the go fast machine. I think that should be the other way around. The MTB could easily become the jack of all trades bike, but a go-fast weekend bike? Maybe with a set of slicks, but its a pain to swap tyres all the time, so your option their is a second wheelset, but that may blow the budget.
Have a think about do you really intend to mount panniers and a rack. On some bikes that is just not possible, so this narrows the field down straight away.
Is there one which can do it all? Who knows. The answer is yes, but with compromises in one area or another depending on the type of bike you end up buying.
I have three bikes but would like another which suits my type of riding better than the bikes I've got, and I'm sure there are situations where another type of bike again would be more suitable, but its my old steel framed road bike which gets the nod over the newer alloy framed road bike and the hardtail MTB as the all rounder. I just accept its limitations over things like dirt roads and ride over them anyway.