we did the same and then switched to the native UUID type. it eliminates the need for a unique index and we saw a drop in storage space by 1/2. it's totally worth converting UUID to the uuid field.
ALTER TABLE my_table ALTER COLUMN my_uuid TYPE uuid USING uuid::uuid;
And you want as much of the index as possible in RAM. When the index is 10 times larger than necessary and do not fit in your RAM, you get a very expensive performance penalty!
ALTER TABLE my_table ALTER COLUMN my_uuid TYPE uuid USING uuid::uuid;