I think you will find that your Anyroad gives you just as relaxed a position as your other picks with a flat bar. Assuming your Anyroad and other bikes are sized by the same methods for your current height, inseam and anything else you wish to go by.
I'd just not like giving up the extra hand positions given by a drop bar. They come in handy for me on long rides even when I'm not trying to be as fast as I can be. Possibly you might just need to shorten the stem on your Anyroad if you are feeling stretched out too much. Or if the bars have a lot of reach built into them, then there are also short reach drop bars that might help with that too.
Welcome to BF