The booster would not exhibit the symptoms you indicated
-very squishy
[booster will make it squishy as opposed to not having one]
-vibrating (felt like a gravely feeling, if that makes sense)
[booster is all about pedal feel, if the pedal was vibrating maybe]
-had to floor the pedal to get it to even try and stop
[if the booster was bad, you wouldn't be able to floor the pedal if you ever had a car on a hill and you lose the booster the problem is not putting it to the floor, it's "how can I push hard enough to get it to the floor Iiiiiiiyyyeeeeeeeee...".
So I think you have a caliper rpoblem, possibly warped rotors, possibly dragging pads making the rotors hot and fading them.
Stop the car when it's hot and lift the front end if the wheels are hard to budge, then you've got a caliper problem, if the wheels move freely, take one off and check the pads, if the pads look good and the rotors are not scored, then it's ok. You might have a cracked pad, that would do it, or one that's gone completely.