Isn't there a restriction on how much of a period difference you can use when using the rayleigh method?
Yeah.... Table 12.8-1 of ASCE-7. You can use a period of between 1.4 and 1.7 times the "approximate period" to get your base shear, depending on the Sd1 of your site. I am skeptical how this could be properly applied and get a 1.7 force reduction in the type of structure you describe. That just seems like higher of a force reduction than I'd expect.
Also, I question how much of these provisions have really been "tested" with the taller wood structures that we're seeing today. Heck, I question the deflections that we calculate for wood shear wall buildings too.
I'm not saying that you're wrong. Just that something sounds a little off and that this is something that might require some caution.