I tested SteemSQL but the searches were extremely slow for some reason, whereas on SBDS MySQL they took milliseconds!

The reason is very simple: there are no indexes on author and permlink on the TxComments table in SteemSQL.

This table is rarely used and creating indexes on these columns will consume (waste) a lot of disk space because of the length of permlinks. That's why you got a huge database after dumping the blockchain into your MySQL database.

Should I add those indexes, you would get the same milliseconds results, like the one you have on the Comments table.