The Alto Digital 1604 is a very capable mixer for the price.
I particularly like the compression on the first few channels and the ability to solo channels (I don't know if this is capable of being PFL or whether it is AFL).
The channel - group (sub) - main structure can be useful as well.
Because the music market is so much bigger the price for features is lower for music desks.
I like the Allen & Heath XB10, like many people, if they did a version with linear faders I would buy it.
I'm looking forward to someone making a radio surface for something like the Behringer XR18. A few physical faders and buttons and a configuration would do it.
For radio a few clear controls and everything else hidden is the best for self operation.
Having given the problem a little more consideration, I'm more inclined to recommend first trying a software mix (Skype etc.) and making your mixer a single connection to that conference (via a PC obviously).
I would also look at Google Hangouts and the Hangouts Toolbox https://www.hangouttoolbox.com/
Irrespective of the means of connection of the call, as you have identified you need two "mix minus" or "clean feed" busses.
With "big" mixers it is possible to produce multiple mixes but it gets unusable for a "self op", you need the brain of a sound supervisor to drive a desk like that.
You are really in the territory of a "proper" broadcast mixer to get something for "self op" that does what you want rather than something like the Behringer.
It is considerably more expensive, but the Allen & Heath XB-14 would be worth a look.
Sonifex also have excellent products which can do what you want but they will be more expensive than the Allen & Heath.
An alternative (not very controllable) would be to Skype conference the 2 remote callers and then bring the composite in on a single mixer channel.