As promised, here is a simple way to test the booster along with few tips. I'm 100% sure the booster is not your problem, but knowing that you changed it and knowing it costs $500, I'm going to post very simple brake booster tests, so that nobody in the future will change one unless they have to.
Few facts first:
1. Brake booster NEVER creates a soft pedal.
2. Brake booster NEVER creates a low pedal.
3. Vacuum problems (PCV and other things people change when the pedal is soft) would NEVER create a soft or low pedal. Tip: nice way to test for vacuum problems in the paddock is to pull a healthy Miata alongside and moving over the vacuum hose.
4. Brake booster always creates.....that's right, a HARD pedal.
Three brake booster tests:
Test 1. (Operation).
Engine Turned Off. Pump the brake and hold the pedal down. Start the engine. Pedal must go down a bit. If the pedal does not go down booster is not working.
Test 2. (Air Leak Check)
Run the engine for 5 minutes. Turn it off. Press the pedal about 3 times. Each time you depress it, wait about 6 seconds. If the brake pedal "goes" in less and less with each pump the booster is air tight.
Test 3. (Air Leak Check under pressure)
Start the engine. Pump the brake. Stop the engine and hold the pedal for a minute +-. If the pedal position does not change all is good.
This is not a complete test for the booster, but a good start.
OK. I swear swear swear I am not trying to be "that guy" on the Internet that argues over nothing based on some esoteric counterpoint, or just because I think I am the Grand Poobah Of All Braking Knowledge. Please believe me. I learn things about braking every day from all sorts of people, and I share the following rambling in an attempt to be helpful. I am not trying to be argumentative or crap on your suggestion, which has a lot of merit and sound reasoning.
What you say above is (more or less) true ON PAPER. If we put force and travel sensors on the pedal, your test protocol will succesfully exclude the booster, most of the time. But - I have seen countless - seriously I cannot count how many times - brake complaints that would pass your tests and that are still directly attributable to the booster.
Why? Because we, as human beings, totally suck at accurately perceiving and reporting what we THINK we feel in our foot. I have had people - car enthusiasts, mechanics, engineers, racers - swear on their loved ones' graves that they have "spongy pedal", "no brakes", "brake failure", "sudden fade", etc., never thought to be a booster issue, all of which turned out to be the damn booster. When power brake assist comes and goes, our foot and our brains interpret it as "brake failure".
In short, if vacuum (and thus power assist) comes and goes, then pedal hardness SEEMS to come and go. Going from no assist to lots of assist feels the same as "spongy pedal". Guys that track or race turbo cars with no vacuum pump will know what I mean - you get to the end of the straight, pedal feels like a brick but you aren't stopping, then suddenly the pedal gets "sucked" down and you stop like mad as power assist is restored as vacuum builds.
Some anecdotes:
1. Myself - using something akin to your test protocol above - was completely convinced that I did not have a booster problem on an old Datsun Z I was restoring. I bled and bled and bled and drove with power assist disconnected and pumped the brakes with the engine off and installed pressure gauges and replaced things and made myself miserable, until I discovered the reaction disc fell out of the booster during cosmetic "restoration" of the booster. I would have sworn to you that it wasn't a booster problem, but it was. Why was I wrong? Because- again - we humans are TERRIBLE "transducers" when it comes to perceiving and reporting what we THINK we feel in terms of pedal force and travel. I thought I was above that and smart enough to know better than everyone else - but I wasn't. I was completely wrong. What I thought I felt and what I thought was happening was dead wrong, despite 15+ years in brake engineering. It was the damn booster the whole time, and I refused to believe it. And thus, I spent 6 weeks wasting $100+ of premium fluid and compromised paint and irritated skin racking my brains out trying to figure out why my brake feel was soooooo intermittent and soooooo bad when there was no problem before I decided to cosmetically "restore" everything. Still pisses me off today!
2. A customer of mine SWORE SWORE SWORE SWORE TO GOD that he had "spongy pedal", "air in the lines", "gotta pump the brakes to stop after a few laps", etc. Get this - NO BOOSTER at all on this car. He bled everything, adjusted the bias bar, added cooling, upgraded fluid boiling point, installed pressure gauges, etc. Same complaint. Without really telling him what I did, I did nothing more than raise the pedal 1/4" or so with a yoke adjustment. No complaints in 3 years since. How can that be? It isn't possible physically - it is only possible "mentally".
My only point here: Humans, even experienced racers, brake engineers, and people that are both - really really suck at perceiving and reporting what is happening under their foot. We detect changes in feel and performance very well - but we are terrible at inductively (or deductively) determining what it is we actually feel, much less why we feel it.
In any case - I'm very curious to hear if the problem gets fixed and what is reported to be responsible! 