Would you call this a defamation of character campaign, or would it be a smear campaign?

Both and I can empathize with you, I have a close friend that his ex wife spread rumors all over a small midwest town that he was a child molester, no charges have ever been filed and it is false, he is denied access to numerous facilities the type of which you mentioned and he has a terminal disease and cannot go to the local Hospital, the people who have spread the rumor should have taken into consideration that with a terminal disease he already has a death sentence so his retaliation has no limits. It is impossible to disprove false Information like you are describing and you either have to hope it goes away or relocate. A lawsuit is usually not an option because most lawyers want a large retainer and most cannot afford to pay it.%&