The issue here it is not the correct spelling of the title "Paramhansa", but the possible forgery by SRF of Master's signature. In that book, SRF only explained (more than 20 years latter!) why they changed the spelling of the Guru's title, from Paramhansa to Paramahansa. Curiously, they did say at that explanation that Master used sign his name in both ways, as some people here think.
The last part of your message is very sweet and true: SRF, Ananda, Solar Logos, CSA, etc, are indeed "offshoots of the Guru's wonderful family".