"...Interestingly, the pedal is firm with the engine off, but soft with the engine running...."

That means the vacuum booster is working properly - no prob.


",,,Brake failure light is on intermittently. ..."

For safety/redundancy there are two completely separate hydraulic circuits in your brake system. If one circuit fails for some reason the pressure imbalance between the two circuits moves a little shuttle switch that triggers the failure light. It might be that they bled one circuit but not the other. Each front caliper has at least two bleeder valves and they both need to be bled. It sounds like you're suffering diminished stopping power because only one circuit is working right.

Note: On some cars, once the failure light is triggered, you have to unsrew the momentary switch from the junction block and use a small screwdriver or awl to re-center the shuttle. Of course if this is the case you would re-center it AFTER fully bleeding both circuits. Since your light is intermittent it may be re-centering itself OK.