While I don't have any written sources to back up what I will say however I think it's still worth stating...
I'm not so convinced that there is a problem of making a leishiv and then leaving the Sukkah to go wash. The minhag is as brought down in Shulchan Aruch Siman 643 to make the bracha leishiv by kiddush. Leaving the sukkah to go wash ones hands is all l'tzrich the seudah and v'dei the leishev is going on the mitzvas that one will be doing now in the sukkah (eating, sleeping, learning, "tiul", etc.)
Many do have the ability to wash in the sukkah itself or perhaps right near by making this less of a problem. However someone who lives on the 4th floor an an apartment building and builds their sukkah on the street can run into this problem.
However that which people adopt the minhag that the Rema brings down makes a lot of sense. It takes care of the problem as well of being a hefsek between washing and hamotzei which is also a problem (perhaps even more so then being mafsik between the leishev and the start of the seudah.) It's also more convinient as to not bother the family and guests to go back into the house to wash for the seudah especially in a situation where the sukkah is far from the house. Being somach on the Rema (even if others argue) in such a situation I believe is perfectly ok. I heard b'shem Rav Padva (from England) that one can always be somach on what is brought down in Shulchan Aruch when it's needed.