Deal with exclusions before you buy the insurance. Exceptions to title insurance coverage are set forth in the title insurance commitment.
Conscientious consumers will read the commitment, including the jacket, and ask questions until they are satisfied and understand.
Conscientious title insurers will provide a copy of the title commitment with pertinent attachments to the purchaser automatically and without delay.
Conscientious consumers will DEMAND a copy of the title commitment before closing so they CAN deal with exceptions before buying title insurance.
Conscientious consumers will FIRE creepy title insurers who refuse or cannot produce a title commitment and answer questions about coverage prior to closing.
So, if unfortunately you are stuck with exclusions or exceptions that make you unhappy, think back to whether or not you were given an opportunity to review the title commitment before you closed.
Even if you were pushing for a fast closing and got the commitment at the table, you still had the chance to postpone. [Some folks push for a fast track closing without considering potential damage to themselves.]
If you had NO opportunity to consider these exclusions/exceptions before you purchased the title insurance, I think you should have a chat with the title company and if necessary hire an attorney to have that chat for you.
If you were given an opportunity to review the commitment and didn't or didn't ask questions, shame on you.
As a post script I have to say I'm not sure if I caught the right drift with your query, so if I'm off target, try again. ;)