The specification of gain accuracy is different from the specification of linearity for such an input.
You should use a good x100 probe to look safely at a +/- 150 V swing.
If you use a x10 'scope probe, check its maximum ratings carefully before using.
Within the maximum ratings of the probe and the DSO, the linearity should be far better than 1.5%, even though the absolute accuracy of the measured voltage is only guaranteed to 1.5%.
Spectrum analyzer: normally, a SA has an input impedance of 50 ohms, and is used with 50 ohm matched attenuators to measure high power signals: +30 dBm in 50 ohms is 1 W, or 7.07 V into 50 ohms.
Probably, your high-voltage amplifier is not designed to drive 50 ohms: 300 V pk-pk into 50 ohms is 106 V rms, or 225 W mean power for a sine wave.
If you use a high-impedance 'scope probe (usually 10 megohm input impedance), be sure to adjust the compensation with the DSO (see manual) to get a flat response past 1 MHz.