If you're certain about this plastic-tipped bullet thing, then you've definitely not gone deep enough. Sometimes just backing off a grain or two of powder, or switching powder or changing the depth of the bullet seating by a few .001" gets you where you want to be.
I had a finicky Rem 742 that only liked this off-brand South African ammo. I bought as much of it as I could-- I still have a few boxes left. Anyhow, as soon as I got into reloading, I tried a load in it that was originally built for my M1 Garand. Bingo! It was a tack driver all of a sudden. What's more, I tried 2-3 other loads in it and found it was a fairly accurate rifle overall. It just liked a moderate powder like IMR4895.
You know, you MIGHT actually be able to afford reloading. Check this out:
Now, that would not be all you'd need, you would still need dies and consumables, but . . . you see my point. You could get into reloading for one caliber for just the cost of a couple boxes of that fancy ammo you're buying.
Here's the book that got me started:
The ABC's of Reloading by Bill Chevalier
Just got done reading/rereading several sections of this book.