Ok, Zack, I don't know you, so don't take this the wrong way. If properly installed (Check Les Andrews book, or some other diagram of the spindle assembly for details) the Snyder kit fits. I'm guessing you've got something assembled incorrectly, or that you are perhaps driving the pin in rather that drawing it the rest of the way in with the spindle bolt nut. When I assembled this same kit, the bolts went in far enough to get a solid start with the nut on the other side. Then, by tightening the nut I was able to draw the bolt in until it was most of the way in. It does not need to be flush with the front of the axle, just securely in place.
The bolt fits the pin and then as you draw the nut tight the bolt cinches in nicely. So, the things, I'd check are that the lower side of the upper bushing, and the upper side of the lower bushing are flush with the spindle i.e. no taking up excessive space. Check that the bearing is installed open side down, and likely with two shims between the bottom of the bearing and the axle so that the bearing outer casing does not turn, in other words is snuggly fit so that the weight of the car will be resting on the bearing. After you've gotten that felt grease washer and cup in between the bottom of the axle and the bottom of the spindle ( a hassle, by the way) the whole assembly with king pin in place should be quite snug.
If you think I can be of further help, PM me and I'll give you my number. We'll talk on the phone.