I have just picked up your thread about your game pie. I make raised pies several times a year as our family and friends love them. I have learnt that the best way is not to pack so much filling in as you would like. I leave about 1 inch ( yes, I'm that old!) space lower than the top of my pie and then with the natural shrinkage as well you should be fine to pour your stock in the hole. Actually, I sometimes make 2 -3 holes and cover them loosely with a pastry shape ie. leaves or roses (if you are feeling the vibe?) which you can lift off, do the business and replace for presentation and that works well. I haven't found a 'tool' as such myself for this purpose.
Anyway, good luck. Bye the way, if you find that you have some filling left over, then make a dinky one for lunch and/or freeze for another time.