I noticed a huge change right when Gwen started trying to convice Richard that she was Hazel and from there out. Where did you see the the other break or change in style?
You really need Number of the Beast to flesh out the ship called Gay and her capabilities. That one would help with Hilda, Jake, Deety, and Zeb, along with his multiverse theory too. Without that one in mind, I would see the final part of the book as you did.
I enjoyed Richard and Gwen too, an obvious example of his uber-capable characters...even with his amputation. I've heard theories that Richard and Gwen were supposed to be overstated representations of Heinlein and his wife...Richard Ames (RA: Robert Anson)...Gwen Novak (GN representing Ginny which is how he referred to his wife). I normally would laugh at these reaches, but after all of the black hats in The Number of the Beast being anagrams of his name and his World As Myth theme...maybe its not such a big stretch after all.
What did you think of Bill? Was he purely a plant to allow him to express his political views? If so, what did you think of those? If not, what was the point of Bill's character? Was he supposed to be purely on that plane, or was he supposed to be a member of the other "Time Manipulator" groups?
What did you think of Richard's thoughts on homosexuality and plural marriage, etc.? What do you think Heinlein's motive was for including this stuff? Did he have a point...or was it purely to titillate the reader?
In hindsight, I'm really wishing I had reread a bunch of Heinlein's other works before pulling this one out again. I wonder how many references to other works I missed beyond the ones that I caught, just because I haven't read them in a while.