It seems to be impossibly hard to make it so that when a TabStrip is in a container that the content area is able to fill the remaining space rather than fitting to the content.
I have seen that there are work arounds for what appears to be the same issue for the jQuery KendoUI library but it looks like a hack rather than a true solution. (One shouldn't have to go to the code behind to make this happen).
A simple "fillRemainingSpace" (or similar) would be perfect and have the TabStrip handle the rest.
I expect this is pretty common scenario for anyone making application like UI websites.