In seven instances two letters are 'moved outward', brendan - I don't think it gives away too much to confirm that, 'outward' means they move to the two outer circles of the grid.
But the letters that move can travel any distance to do so (and even the last letter of a word can appear to move 'outward' because the first moved letter must squeeze in between this letter and the letter that actually precedes it in the answer - this is the case for two of the answers).
Remaining letters stay in their original order, and moving letters remain in their original order - so if the word 'DoCtor' is to be treated you'd enter 'otorDC'. I hope this helps.
I was too peeved when I finished it to mention that I found it a clever puzzle and (for me, at least) a completely novel idea. It must have been as hard to set as to solve.