One problem with giving any advice is not knowing the type of data or the search type you need to do. It isn't surprising that MySQL would do simple count or even search faster than pg.

If you are doing a unique key search, then count is either 0 or 1. If you are doing a text match, then a unique key index isn't going to help much unless it is 'abc%' type. With the low size of 64chars, tsearch might be a very fast index and even pretty efficient on storage.

Another point about using tsearch: you should be able to make a copy of the table, add the tsearch column and create the index anywhere. Since the index is part of the row data, this is possible and easy without some hack involved. Then you could copy the data back into the original table, modified. You may have to go offline for a brief time, but you should be able to do all this testing without interfering with the live site.