Why does my summing mixer max out at 5.39V when my rails are roughly +/- 11.7V?
Your mixers divide by 4 which limits your output signal from each input. If you wanted unity gain, you simply change all the 47.5k to 12.1k. Of course if each input were maximum then the sum of all inputs may exceed the supply range at some point if the peaks are in sync, so you need specs for “ headroom “ to limit the maximum input.
The Schottky Diodes clamp the input at ~ 350mV @ 1mA above 3V and below -3V with unity gain after this.

the LM324 may get close to Vee but has a 3V drop from Vcc (full temp range with 10k load) due it’s high side Darlington driver and bias. See [datasheet1 “Electrical Charactersistics for Voh=27V typ. and Note(1) Vcc=30V

therefore you have designed it for a +/-3 V + diode clamp Vf. If you wanted 8V then you would need to change the clamp diode reference voltage or R input ratios or output gain.