Severe overmodulation will cause the transmitter's final stage to feed harmonic frequencies into the antenna, but only when you modulate.
The RF energy in those frequencies is not anywhere near the frequency your antenna is tuned to operate with. The SWR meter gets fooled into that high reading because the SWR at 54, 81, 108 MHz and higher really is high.
Even if the SWR at 27 MHz is low.
If the mike-audio compressor-limiter transistor TR32 has been removed, this will allow severe overmodulation and produce enough RF-harmonic energy to do what you described.
The antenna is not misbehaving, it's the quality of your transmit signal that's causing the high reading.
73