To make your BC really white without adding coloring...whip the dickens out of the butter and shortening when you're creaming it. Let it go and beat it for at least 5 minutes. See how white it gets.
I've also used Americolor's white gel paste. I layer my frosting on and chill between layers to harden. Then when it is time for the last layer is when I add any colored buttercream that I've mixed. You avoid any weird taste by having a thin layer of colored buttercream as opposed to the whole thing being filled with food color. I do that for ALL colors of BC. Not one of my cakes that have a lot of color are solid colored buttercream throughout. Saves on food coloring too!
Oh... and you said you couldn't get sharp details on your
all- butter BC piping because of your 'hot hands'...well I have them too. I don't do a whole lot of piping, but when I do I keep two bags handy and when one starts getting too soft, I put it in the fridge for a few minutes and use the other one until I need to change it out too. Keeping some really cold water close by to put your hands in periodically can help too! Just an FYI!