So, you must use the ability after playing it?
Yes, that is the way it works. The targeting must occur immediately after the card is played, on the same turn, on a creature. Since it is a curse, you cannot opt out of it and wait for later. It must be used immediately, and fully unless it is destroyed, then the curse only lasts upon the creature still cursed.
It is very interesting. I like the idea, and of course death is the only thing balancing it. I feel like with added bonus for upping, the cost should stay the same.
Do you suggest to add another benefit to the upped version, or to keep the upped cost at 3
?