I'm pretty sure I used a puller type with the screw in the middle too. My memory is not giving me a very clear picture though! I think the only puller type I own is a centre screw, so can't see how I used anything else.
I can't remember if it was this repair job or another, but a few times while using the puller I've had to put some extra pieces in the puzzle. Eg. a socket or spanner in the middle, depending on what edges you have to screw against. Do you have it apart? Photos are always helpful. I can't remember what it looked like now.
Otherwise, maybe someone else reading can jump in here?!? :)

