If you look at the plate-cap connections on the four final-stage tubes, you'll probably find ONLY a skinny bare wire joining each of the four cap clips to the ceramic pillar (plate choke) at the center of them.
When it was built, each of those bare wires had a ferrite "bead" slid over it. These served as parasitic-suppressor chokes. Trouble is, they would get hot, split apart and the broken pieces disappear out the holes in the lower cover.
Most of the time, you'll still see these tiny, black "beads" on the plate-cap wires of the two driver tubes. OR, you'll find a conventional-looking resistor with four turns of wire coiled around it on each of the two driver tubes' plate-cap clips.
Adding a conventional "parasitic choke" with four turns of wire around a 47 ohm 2-Watt resistor to each final-tube plate-cap clip (in place of the bare wire) will usually fix or at least improve this problem.
Without those chokes (or the ferrite beads) the amplifier pumps out additional frequencies besides the channel your radio is feeding into the amplifier. Those 'extra' frequencies will cause the SWR meter to read high, even though the antenna checks okay with the barefoot radio.
Not sure where I have a pic of this 'fix', but I'll look around.
Oh, and about that "recalibrated his meter for the power jump", was playing pin-the-tail-on-the-donkey. His meter is not calibrated any more. No big deal, but the power readings won't be trustworthy, anymore. The extra frequencies will tend to 'fool' a wattmeter, along with the SWR scales.
The meter is only calibrated if he used a 50-ohm dummy load with little or no SWR. No big deal, but the numbers he reads from that meter now are just that, "numbers", not a measurement. In the same way that moving the red line up on your tach doesn't keep the valves from floating at high RPMs.
73