Yeah, those cheap press kits are a total gamble. The problem is that soft aluminum deforms instead of transferring the force evenly, so you're basically crushing the headset in. A proper steel drift set is the only way to go for more than a couple uses. Have you looked at any of the park tool compatible options?
Man, I used to defend those cheap kits to save a few bucks. But you're totally right about the aluminum just smushing. I wrecked a headset on my old bike because the drift bent during the press. Now I see it's worth getting the right steel tool, even if it costs more up front.
Reminds me of trying to seat a bottom bracket with a homemade PVC pipe press. It worked exactly once before the pipe split and left plastic shavings everywhere. My buddy spent an hour picking bits out of the threads with a dental pick. Sometimes the right tool is just the one that doesn't turn your project into a cleanup nightmare.