Sum Across Worksheets To Include New Sheets

A colleague of mine maintains a spreadsheet with a worksheet of data for each month labeled "Apr'07", "May'07", "Jun'07", etc. He then has a summary worksheet that gives summaries of the various data fields on the monthly sheets. Currently he has been using the kludgy method of listing each cell to be summed. (e.g. " SUM('Apr'07'!A2,'May'07'!A2,etc.) Since he is dealing with a summary of about 200 rows by 15 columns this is a big pain to maintain. My first thought was to set up his formulas as a range of sheets rather than naming each; E.g. SUM('Apr''07:Jun''07'!A1)

Then I thought that rather than having to update each formula when he adds a new month, he would be better off having two cells that control the start and end sheet and having then feeding them into the summary formulas using the INDIRECT function.
However, try as I might, I can't seem to get the INDIRECT formula to work. In the attached example spreadsheet I have set up B1 and B2 to hold the names of the start and end worksheets, respectively. So my attempt at an Indirect Sum formula is the following: SUM(INDIRECT(" ' "&B1&":"&B2&" ' !A1"))

(Note: spaces added between " and ' for clarity) When I look at the formula evaluator it evaluates to SUM(INDIRECT("'Apr''07:Jun''07'!A1") and then generates a #REF error. What am I doing wrong here? I'm open to all suggestions of fixes to this method or an alternate method that would achieve the objective of performing calculations on cells across a dynamic range of worksheets.