In your position I would go for the Lavry plus a separate monitor controller. You didn't mention Mytek in your original post - I use their DA96 which is very good, and this has since been superseded by the 192 series. Just another option to consider...
Do you know Coleman Audio? They make very high quality monitor controllers that are in the ballpark price you mention.
Coleman Audio M3PH mkII | Sweetwater.com
I would rather get two great pieces rather than try to find an all in one box to do both (and with an all in one box there is more that can go wrong in it). I think in terms of absolute quality this would be the way to go if I were in your position.