A couple of suggestions I have for you:
Using hard silver solder for this sweat soldering operation is going
to be really tough. If you can use medium solder, using less heat,
you will have a far easier time of it. Another suggestion would be to
get both pieces perfectly flat, before you melt the medium solder
chips on the back side of the smaller piece. ( make sure it doesn’t
warp from excessive heat!) As long as both remain flat (except for
the melted pieces of solder) you should be able to put both pieces
together, flux, and heat with a broad flame, heating as evenly as
possible. I’d recommend a sturdy, flat screen, and heating from
below. I try not to use any cross-locking tweezers, etc., as they can
create more of a problem.
I have a few pieces of 1/4 in. wide square steel rod, cut into 3 in.
lengths. If I have a problem holding down a large flat project like
this one, I’ll weight the pieces down with a piece or 2 of the square
steel rod. They don’t absorb much heat, and serve to hold pieces down
gently when soldering.