I thought I figured it out but apparently not.
Since my board has two soundcards installed, I ran tests. The problem is that the second chip isn't turned on (first one is always turned on), yet my system is supposed to check each chip in turn.
So I did a simple test. If I remove the chip from the left (chip U$1) from the circuit (as in remove the chip from its socket), then the system will think the chips are missing even if the chip on the right is inserted. If I insert the chip on the left, then the system will think both chips are installed regardless of whether the chip on the right (chip U$2) is present or not.
So I did some voltage measurements while the left chip was inserted and with the right one (U$2) not inserted.
For the inserted chip, the voltage measurements at its SS are 0V, then 1.91V.
For the removed chip, the voltage measurements at its SS are 4.97V then 0.04V.
I deliberately slowed down my program so that my cheeeep multimeter can read the voltages.
What am I doing wrong? Is R3 supposed to be lower? I want to use as little current as possible yet still have this transistor as an effective inverter.