Improve tests for ledger storage based test cases

*Motivation*

In #1218 , we test multiple features (e.g. piggyback lac, explicit lac, long poll) with different ledger storage implementation. However those tests are fully end-to-end tests, which is kind of expensive and redundant. It would be good to think of how to improve them.

Start by reading issue #1218 and its end-to-end tests for piggyback LAC, explicit LAC, and long poll across the ledger storage implementations. Identify which coverage is redundant and determine how the cases could be tested without fully end-to-end execution. Done means the relevant behavior remains covered with less expensive, less redundant tests.

Written by the indexing model from the issue text.