Selling partial holdings is a frequent tax topic on the IV MLP board. I've never sold a partial, so it's not been an issue for me and I don't know those rules re cost basis. I go to this site to get K1's and estimates on selling implications from time to time: https://www.taxpackagesupport.com/
I have to wonder how many people regretted decisions to buy MLPs given the added tax-preparation complications. But it's such a sweet deal with the tax-deferred business. AFAIK, cost basis is something that the individual investor still needs to track. Unlike stocks and REITS, no help from the brokerage firms. Digression: I've never held a REIT long enough to have the cost basis go to zero through return of capital; my guess would be that the brokerage handles the tax issues automatically if that happened, but IDK.