I think the problem is how the potatoes are being poked, and maybe in how they are "boiled".
If done well, then the potatoes should not split and cause trouble with cooking.
To do this correctly, you want to use a very sharp knife with a thin and not too tall of a blade. Typically, I use a paring or boning knife.
Select a potato to be tested. It should be the one of the largest ones being cooked.
Remove the potato to be tested from the water with a pair of tongs.
Line your knife up with the potato so the height of the knife is the longest axis (so there's as much potato above and below the knife as possible).
Stab straight into the potato, about 2/3 to 3/4 of the way into the potato. Do not go all the way through the potato.
Lift the knife, with the potato pointed down, and possibly shake the knife slightly. If the potato comes off, then it's done.
If the potato does not come off, then you want to use the tongs (or a folded over dry paper towel) to grab the potato and pull your knife straight out. You could also slide a fork around the knife to push it off. Do not cut into the potato to release the knife.
This will leave a minimum amount of damage to the potato, and shouldn't cause it to split in half or significantly affect how much starch leaches into the water.
This also assumes that you're only doing this a few times. If you're testing more than 3 times, you may need to wait longer before your first test, or longer in between tests.
If you're cooking extremely small potatoes, then it might be difficult to find a potato that's sufficiently larger than the size of your knife.
You should also be simmering potatoes. A rolling boil is not desired, and the agitation of the potatoes may cause more starch to be released. Once the water comes to a boil, turn the heat down so you're only getting an occasional bubble coming to the surface of the water.