You can use the trim/extend command in the weldments toolbar to butt up to any surface.
Or you can convert entities of your profile at both ends of the RHS to do an extrude up to body whilst editing the part in the assembly.
You want to have no gaps in the face contacts to act as a welded part.
This is kind of a tough thing, and it's equally so common a thing to want to simulate. I don't have the answer but you might want to read this: http://www.eng.uwo.ca/designcentre/FEA%20resources/116_Welds.pdf
It's a couple years old now, but it's a really good read to get some insight and it's like 20 short pages so you can go through it in an evening.
Thanks guys for your help.
I've ended up using a combination of things. For some joints I've combined the bodies and added fillets etc to create the appropriate amounts of metal, but in most cases i've just relied on the "bonding" in simulation, as this seems to give quite valid results. Obviously this isn't going to be 100% representative, but it seems it's not really possible when dealing with something like a weld, which doesn't have consistent properties, but it provides a reasonable indication of what the weak points are etc.