If the sunflower seeds are there he will just keep eating them.
At some point you do just need to take them away completely (a bit of tough love), but there may be more than one way of working up to this.
If he will eat from your plate while you are eating then perhaps you can use a bit of trickery. Could you mix in some Harrison's with what you are eating - perhaps on the edge of the plate so it doesn't ruin the meal. You could eat it too (I have) but the taste and texture is not exactly pleasant.
You can also try enticing/teasing him a bit with some pieces of the new food and then handing it to him. He may drop it right away, or perhaps crunch it up but drop the pieces, but at least that's a start. Birds have to become familiar with new foods before they will eat them.
All the while when trying these ideas leave some Harrison's in his cage and gradually reduce the sunflower seed allotment. Perhaps on the first day he gets a handful of sunflower seeds in the morning, the second day slightly less than a handful, etc.
I suspect when he gets hungry and runs out of sunflower seeds he will be angry, cranky, and he'll put up a big fuss, but I HIGHLY doubt that he will stay hungry when food is there.
How long is safe to leave him on his 'hunger strike'? I'm not sure there is a specific answer - if there is your vet could advise better - but as I said he will not starve if there is food there. Birds can certainly go a day without eating, or more depending on their condition.
Anyhow, I'd recommend gradually reducing the amount of sunflower seeds he gets each day so he will get some nutrition and not starve but he will be more and more hungry and motivated to try the new food. And once again he will fuss and be angry but you can't give in to his temper tantrums.