The SPICE simulation will only be as good as the models for the valves are, and the model for the transformer. Apparently some people have had success with LTSpice/SwitcherCad (which is free), and possibly CircuitMaker, though I personally haven't bothered to learn how to use either.
There was a time when all these things were designed without the aid of computers, and many people still do. You will likely get better results by having a look at the
curves, and using the general principles for minimising distortion such as choosing an appropriate operating point. Note that you can approximate the distortion by preparing composite curves after choosing the operating point from various formulae, but this can be rather tedious.
Choosing an appropriate operating point and load impedance, then fine tuning it in an actual prototype (you could build a notch filter, or use the computer sound card for distortion measurement) will be far more accurate than the computerised simulation, and may well give a better result.