Ah, if you were to set the Load control at the halfway point, and then turn the plate-tune knob that's been moved to the front, will that knob show a peak at all?
It sounds to me as if the amplifier is being peaked not at 27 MHz, but at the second-harmonic frequency 54 MHz.
I would first try setting the Load control at the halfway point, and then turning the plate tune control to see if it will show a peak.
At least that should get the output circuit closer to 27 MHz.
The usual means of "fine-tuning" to get a proper peak on the plate-tune control is to tweak the output coil connected between the tune cap and the load cap.
First step is to determine which way to tweak it, for more or for less inductance.
The position where the tune control shows a peak is the guide for this.
Might have a look to see if any disc capacitors have been wired in parallel with the Load control. Would affect where that knob shows a peak.
73