I have a small Hardinge gang tool lathe with 5C and use homemade nylon pullers with no problem. Get yourself a 3' length of 1-1/4 and bore the hole ~.025" under size then use a hack saw and cut a cross in the front to allow it to expand over the stock.
You'll find that if the stock a little over sized a standard puller will shove the stock into the collet as opposed to slipping over the bar.
I do a lot of 1/2" x 4" aluminum stock with 1.0" M10 threads on the end. Start 1.25" frrom the collet, turn and thread, use the puller on the threads, pull and finish the OD and part off.
Make a bunch of blank ones to have on hand and bore as needed. Sure they will wear out over time but make the head about 1" and when the tip wears, face off the worm area and good to go. I have some that I have been using for years and still in good shape. I use .75" brass bar stock to make mine. The only thing I don't like is it takes a tool position. I drill the puller approx. .015" under the stock diameter of the needle valve, and put a generous radius on the entrance. Then a .025-.035" or so slitting saw on the mill about 1" deep or so. Unless the part is critical for length to diameter ratio, having .2" sticking out of the collet should be all you need.
Perhaps your collet closer has more travel and extends your collet farther than it should.