The problem here is that horns won't fit the budget, unless you get lucky with something used.
I think you can find some ZU Audio speakers in that range. They are about 10dB more efficient (when you do the math, the sensitivity of the Viennas comes out to about 88.5dB; this is due to their impedance). That will solve your power issue.
Now impedance plays another role- that speaker has a lower impedance in the bass frequencies- which means the amp works harder to drive it. If you are using the 8 ohm tap, the output tubes are seeing a load impedance that will cause them to make less power and more distortion.
On top of that, lower efficient speakers like this exhibit a phenomena called 'thermal compression'. This is where the speaker voice coil heats up due to the power needed to drive it. Its a measurable and noticeable effect. All lower efficiency speakers exhibit this phenomena; the greater the efficiency the less thermal compression. As well this particular speaker was designed to be driven by a solid state amp (this is revealed by the impedance curve which is low in the woofer region); IMO/IME you have a mismatch between the amp and speakers.