If a higher sample rate can't happen would better filtering be a potential solution?
Once the higher frequencies have been reflected back to the audible range, it's too late : you can't filter them without also filtering "real" frequencies (the harmonics of your sound).
A filtering that would work would need a higher sampling rate : you would then naively synthesize your "sharp" signal at 4x your final sampling rate, let's say 192kHz. Then, you would apply a low pass filter to remove everything above, let's say 20kHz : so now your 192kHz signal does not contain anymore frequencies that can't be represented by a 48kHz sampling rate. You can then peacefully downsample it to 48kHz, aliasing will not occur. So you see that to apply this method, you need to work internally at a higher sampling rate.
Please note that there are A LOT of other methods to simulate an oscillator, this one being the simplest! I don't know how the Virus works. For example, another method works by synthesizing all the harmonics (sines) and then summing them together. So basically, as you're summing sinusoids here, you don't have to worry about aliasing. This method, compared to the previous one, would benefit a lot less from a higher internal sampling rate.