I really wouldn’t worry too much about stalks, particularly in what is softer hay anyway. It’s different with first cut Timothy (as that is all about the stalks) but in things like meadow the stalks are fine and actually some piggies quite like them.
I would also say that even if you find a nice soft batch of hay this time, it doesn’t mean it will be next time - hay varies batch to batch, year to year.
I will also add by way of hopefully reassuring you that of the four piggies in my life for the past seven years - only two of them have had haypoke (once each). Their hay pokes came from soft meadow hay, so my point is that you can drive yourself mad trying to find the perfect box of hay but it doesn’t mean they won’t get haypoke
(The other two have never poked themselves (touch wood I haven’t jinxed it!) and they are about to turn 3 years old).