We already turned off the tap (look at the link above). It is just unimportant countries like Hungary and Slovakia that still import pipeline gas (and they're not making any friends...) . Would be great to pressure them more. Till this year Ukraine still imported nat gas from Russia btw.
LNG is a fungible commodity that is traded world-wide. Don't see much beyond symbolic value here in refusing it. Trying to enforce a price cap would be great there, but needs coordination.