It strikes me that the sequences could be generated from the pieces
using a stored procedure. (this would save lots of typing)

Also the answer could be got by doing a select on the piece table
with joins the sequence table 6 times with constraints that make the
numbers line up and a where clause that makes each piece unique.

you'll then get a row for each solution.

temp tables, stored procedures...  

Is everything so hard to do in mysql?
 
postgresql has date arithmetic, and intervals with a unit month
which behaves as expected so, (other inverval units like second and
year, but month is the interesting one)

in postgresql, this:

SELECT
 extract(year from m) as "Year",
 extract(Month from m) as "ID",
 to_char(m,'MON') as "Month",
 m as "MonthStart",
 m - 6 - (extract( dow from m) + 1)::integer % 7 as "start",
 (m + '1 month'::interval ):: date - 7 -
   (extract( dow from (m + '1 month'::interval)) + 1)::integer % 7 as "end"
FROM
 (select ('2008-07-01'::date  + generate_series(0,23) * '1 month'::interval) ::date as m) as base
;

produces this:
Year | ID | Month | MonthStart |   start    |    end
------+----+-------+------------+------------+------------
2008 |  7 | JUL   | 2008-07-01 | 2008-06-22 | 2008-07-19
2008 |  8 | AUG   | 2008-08-01 | 2008-07-20 | 2008-08-23
2008 |  9 | SEP   | 2008-09-01 | 2008-08-24 | 2008-09-20
2008 | 10 | OCT   | 2008-10-01 | 2008-09-21 | 2008-10-25
2008 | 11 | NOV   | 2008-11-01 | 2008-10-26 | 2008-11-22
2008 | 12 | DEC   | 2008-12-01 | 2008-11-23 | 2008-12-20
2009 |  1 | JAN   | 2009-01-01 | 2008-12-21 | 2009-01-24
2009 |  2 | FEB   | 2009-02-01 | 2009-01-25 | 2009-02-21
2009 |  3 | MAR   | 2009-03-01 | 2009-02-22 | 2009-03-21
2009 |  4 | APR   | 2009-04-01 | 2009-03-22 | 2009-04-18
2009 |  5 | MAY   | 2009-05-01 | 2009-04-19 | 2009-05-23
2009 |  6 | JUN   | 2009-06-01 | 2009-05-24 | 2009-06-20
2009 |  7 | JUL   | 2009-07-01 | 2009-06-21 | 2009-07-25
2009 |  8 | AUG   | 2009-08-01 | 2009-07-26 | 2009-08-22
2009 |  9 | SEP   | 2009-09-01 | 2009-08-23 | 2009-09-19
2009 | 10 | OCT   | 2009-10-01 | 2009-09-20 | 2009-10-24
2009 | 11 | NOV   | 2009-11-01 | 2009-10-25 | 2009-11-21
2009 | 12 | DEC   | 2009-12-01 | 2009-11-22 | 2009-12-19
2010 |  1 | JAN   | 2010-01-01 | 2009-12-20 | 2010-01-23
2010 |  2 | FEB   | 2010-02-01 | 2010-01-24 | 2010-02-20
2010 |  3 | MAR   | 2010-03-01 | 2010-02-21 | 2010-03-20
2010 |  4 | APR   | 2010-04-01 | 2010-03-21 | 2010-04-24
2010 |  5 | MAY   | 2010-05-01 | 2010-04-25 | 2010-05-22
2010 |  6 | JUN   | 2010-06-01 | 2010-05-23 | 2010-06-19
(24 rows)

how it works.

in the calculation of "start" above

 extract( dow from m)
 
   is the day of the week (0=sunday)
 
 (extract( dow from m) + 1)::integer % 7

 is then number of days since since saturday
 (0 if the first of the month is saturday)
 
 so subtracting this many days from today will give the saturday
 after the last friday in the previous month
 
 and subtracting 6 more days will give the sunday before the last
 friday of the previous month.

Bye.
  Jasen