"Yet when the first Lazarus steals two crystals, Kirk exclaims that with them missing, the ship cannot operate at full power. Of course, even with the theft of two more and the apparent loss of the energizer room, the ship still retains the ability to orbit, to beam people up and down, and to fire weapons... But it does appear as if a fairly large number of (paddle-type) crystals are needed simultaneously to yield "full power". Not so many that two would represent an insignificant fraction - but not so few that loss of two or even four would completely deprive the ship of power."
Interesting theory, but let's take a look at "Mudd's Women" again. They burn out 3 dilithium circuits and immediately have to switch to battery power. Then
, they discover they have a spare but flawed one they can somehow make work. In the meantime the entire ship relied on "battery power" and was still capable to beam over the three Women.
The events in "The Alternative Factor" could be much alike. The ship is on "battery power" and will allow Kirk and security personnel to beam down and back up. They recover the two dilithium circuits, put these back and thus have a) warp and b) phaser capability to destroy Lazarus' craft.
I just took a second look at "The Paradise Syndrome". While Scotty was concerned about the deterioration of the dilithium circuits, his major concern were the warp engines:
SCOTT [OC]: We'll burn out the engines!
SPOCK: I want full power, Mister Scott.
SCOTT [OC]: Don't ask for anymore warp nine speeds, Mister Spock. Our star drive is completely burned out. The only thing we have left is impulse power.
It appears they were stuck with impulse power not because the dilithium circuits failed but because of physical damage to the warp nacelles.