Agreed, calling micros() on Teensy LC will probably give performance similar or better than that AVR code.
But if you really want to mess with timers, the register similar to TCNT3 on Teensy LC is FTM0_CNT. And FTM0_MOD is similar to OCR3A, giving you the maximum-1 count number before it rolls over to zero (or FTM0_MOD is zero if the count goes all the way up to 65535).
Here's a very simple little program you can run to see them in action.
Code:
void setup() {
}
void loop() {
uint32_t count, maximum;
count = FTM0_CNT;
maximum = FTM0_MOD;
Serial.print("Count=");
Serial.print(count);
Serial.print(", Max=");
Serial.println(maximum);
}
Regarding TCCR3A and TCCR3B, I'd recommend using analogWriteFrequency() to configure the timer. If you choose one of the "ideal" frequencies it will count all the way to 65535.
https://www.pjrc.com/teensy/td_pulse.html
If you *really* want to mess with those registers too, FTM0_SC is used to configure the timer, including prescaler, and of course you use FTM0_MOD to configure how high it will count.