Another solid episode. Well done!
I'm glad you decided to have default-Ranma try to build a dimension-jump
device instead of using ridiculous martial-arts technique. One question, our
scholar-Ranma sees martial-Ranma in his sleep. What does martial-Ranma see
in HIS sleep? A lecture on quantum physics by scholar-Ranma?
Seems like 5 minutes wasn't enough for you, once refugee-Ranma settles in I
suppose he'll continue his research right? Also, it seems inappropriate for
him to state the following:

Not the Ranma of this timeline, and not the Ranma of his old timeline.

He would simply be Ranma, a fusion of two lives. <<

I take it that this was his only d-jump from his native dimension? In that
case how could he know about the mental contamination issue? Neither of the
other jumpers we know of knew about this until they spent more than an hour
in another's body. With the limited resources at his disposal, I doubt he
could have seen this possibility. I believe you want to justify
jumper-Kodachi's actions but this isn't the way to go about it. It's just
not realistic, I'm sorry.
So can either martial-Ranma or refugee-Ranma put together their own jump
devices? Since their universes are based on ours, they can get their hands
on better computer technology than their counterpart. Of course this is
based on my personal assumption that computer tech hasn't been around as
long in the Imperial universe as it has in ours.
Last but not least I can suggest an 'improvement' in the device. Although I
consider a physical transfer out of the question, it seems to me that a
mind-swap with a transdimensional counterpart is conciveable. Set it up so
that the transfer can take place as long as one party is in a jump device
and it be just cool. What do you think?