It looks so straightforward - cutting bits of wood and nailing them in
(I know it's a bit more involved than that in reality).

Yes, like making sure you don't remove the old ones before enough of the new
support is in! Also, planning how you are going to get the old joists out of
the roof space and the new joists in. You may need to remove some roof
covering and use some sort of crane or hoist, unless you are planning to
reuse the shortened old joists.

Christian.