Honestly, I made that comment without fully thinking through how to implement my suggestion, and now I realize that I've stumped myself. However, let me explain what I meant anyway:
First of all, you're right that this won't really impact your answer at insignificant fractions of light speed. You mentioned that using the 4.72% growth rate, the equation tells you to wait until you've passed the speed of light, and I thought it might be interesting to more accurately model the energy required at relativistic speeds.
So the same way that you used the classical mechanics equation for kinetic energy, E=mv^2/2, ignoring mass and solving for v, to get v=sqrt(2E) and approximating to v=sqrt(E), I thought you could manipulate the relativistic equation similarly.
Now, having gotten a solution from WA, I'm starting to think that I overestimated the effect on accuracy that changing the equation would have. I want to approximate the solution by ignoring some terms or changing an nE to an E^2 or something, but I think that might negate any gain in accuracy.
So to answer your questions more directly, I was attempting to address the error you get when the calculation tells you to wait until you can travel above or near the speed of light, and I only included mass in my equation to try to communicate it to you more accurately, with the assumption that when actually using it you would ignore the mass.
Anyway, I hope I at least clarified my previous comment, even if it turned out not to be very useful! If anyone has a better understanding of how to better model relativistic speeds I'd love to hear their explanation.