There certainly are plain summing mixers available – mainly for modular studio setups, where you have the channel strips seperately; that's a pretty high-grade application so they tend to be rather expensive per-feature. One device with exactly the configuration you're asking for is the Speck Electronics X-Sum. Of course, these devices don't have mic preamps, though. Those are available in 19" ab well, but again mostly aimed at the studio segment.
I think you're better of actually using a full mixer; digital models can obviously be packed to 19" on any scale! And then you can still control that submix remotely from FOH, via tablet or whatever.
The Allen & Heath iDR-32 works great. A bit overkill perhaps. The Behringer X32 is supposed to be surprisingly reliable (though I don't think it's out there for long enough that we can be sure...), maybe the rack version plus one S16 is ideal for your application.
Sure, it still has its cost.
As for DIY... mixing is actually extremely simple, you basically connect all the signals together with decoupling resistors and feed that to a follow-up amplifier (basically one OP amp). Cost: like, 5€. The problem is that you need a stable signal to start with, so this is really all about the mic preamps. With 4 SM-Pro PR8E hooked up to such a DIY mixer you'd stay below 800€ total.