The answer is simple. Re-tune your bow. I was not necessarily tuned correctly before. Good groups can be obtained from an out-of-tune bow in some situations when using a field tip. You made changes and now you need to re-tune in the field. Make double sure the fletching is not hitting anything, put on the heavier tip, and then tune. You should end up with a good shooting arrow if you do everything correctly.

I can get a good grouping arrow without fletching of any kind. You can do the same if the bow and the arrows are tuned corrrectly.