Ignoring that it is an action (which makes it far more powerful), self-counting VP alone is a broken concept. You've tried to correct this by also having an increasing cost. I've thought about something similar and I'm not sure if it works or not. The thing is, the VP is still very strong and cost-efficient. Consider:
| copies in deck| | cost for next copy| | VP for next copy |
| 0 | 3 | 1 |
| 1 | 4 | 3 |
| 2 | 5 | 5 |
| 3 | 6 | 7 |
| 4 | 7 | 9 |
| 5 | 8 | 11 |
| 6 | 9 | 13 |
| 7 | 10 | 15 |
So the very first copy is just an expensive Estate. But after that, it's strictly better than any other VP card. The second copy is Duchy for $4. The third copy is Duchy with 2 extra VP. The fourth copy costs less than Province and is worth more.
Now, in terms of space efficiency (VP/card), it matches Duchy by the third copy and it matches Province by the sixth. But note that it will have cost much less.
In short, I doubt anyone could ever skip this. Until the pile runs out, it makes the regular green irrelevant. You cannot risk letting an opponent get the lions share of these; even losing the split 5 to 3 hurts a fair amount -- that's a 16 VP difference from 2 cards. That puts you down nearly 3 Provinces.
If you raise the starting cost to $4, it's still quite strong as pure VP and probably broken. With the action as well, it's almost certainly too strong.
Again, I am not sure, but I think self-counting VP is broken even with the increasing cost. I don't think there is a point where it just works. Either it is too cheap to ignore or too expensive to be worth the investment. Occasionally it could be a target alt VP for a mega-turn engine, but in that scenario it isn't adding anything new or interesting to the game.
If you're up for it, consider other price points and how they compare to existing VP. I believe I've shown that $3* doesn't work at all, but I did not show my work for $4. So consider that, and consider $5.
