Re: dan book?
Hi, being from Yuishinkai myself I don't have a yudansha book either. But I've have had no problem training with an aikikai dojo and attending aikikai seminars in the US (including USAF summer camp) without one. I asked in the beginning if they wanted me to join the USAF but they didn't feel it necessary if I wasn't intending to test. It may be an issue however if you wish to grade further with the aikikai dojo you are with. Something to ask your new sensei whether they would want you to join their organisation.
I looked into it at the time and rule seemed to be you could join from an unaffiliated dojo as a shodan and then have to wait the required time between dan ranks for each level up to your own rank. ie. if your a sandan with another group, you'd join as a shodan wait 2 years to apply for nidan and then another 3 to apply for sandan. Not sure if tat was USAF or aikikai in general.