Agregar índices de texto completo a todas las columnas de cadena en todas esas tablas, luego une los resultados
select * from table1 where match(col1, col2, col3) against ('some string')
union all
select * from table2 where match(col1, col2) against ('some string')
union all
select * from table3 where match(col1, col2, col3, col4) against ('some string')
...
