Unfortunately wherever you store licence information on a client's machine it's open to abuse (because it's their machine!).
The only secure way to do this is to have your program check in with a remote service, obviously this requires a lot of overhead.
My own approach is that if customers mess with their licence key then they should expect issues and you are under no obligation to assist. I would make sure your key contains information about the machine it's running on (to prevent simply copying the key) but otherwise keep it very simple.
When researching licencing myself I found a philosophy I tend to stick by - you drive away more potential customers with convoluted and difficult licencing setups than you lose through piracy.
My suggestion would be that you reverse your logic - instead of having allowing the removal of a licence key to restart the free trial why not force them to have a licence key to unlock the full application?