No, if there is already a probate that has been completed in that state, you may be able to have the additional property recognized by the court. You won’t need to go through the entire process again.
In Oklahoma a probate in one county is good statewide. So you don’t need attorneys in every county.
If it is producing 3x the annual is a “rule of thumb”. This really isn’t an issue unless you are approaching estate tax issues.