So its totally impossible?
The CCP peripheral in a PIC16F876A can only use Timer-2 as the reference for PWM, so your phase is locked to that.
What do you mean, less ancient?
The PIC16F876A was released in November 2001.
It was just a small tweak to the PIC16F876, which was released in 1998.
In microprocessor terms, that is pre-historic.
PIC16F devices have come a lng way since then.
I vaguely ready someplace else, we could use another timer, 0 or 1 to cause the delay and then turn on the other PWM channel.
The phase is locked to the reference timer. If both CCPs use the same timer, they have the same phase.
Newer PIC16F devices let you select from multiple timers to use as the reference.
Even newer ones have a built in PHASE register.
Is there absolutely no other way of doing so?
With a PIC16F876A?
The only way is to forget about the CCP peripheal, and bit bang it yourself just using the timer, or it may be possible using the CCP in "Compare" mode, generating an interrupt for both edges of the signal.
Not easy at high frequencies.
There are plenty of newer PICs that are pin compatible with the 876A. Can you really not change the PIC?