Something is awry here.

If the last three numbers are like this:

3337888 - Part number
2801 - 10,000 day calendar Saturday, March 29, 1969
261 - unit assembled that day

This would indicate a late 1969 unit.

But that still doesn't look right. In 1969 all of the transmission part numbers started out with 28 or 29 and 3337888 (even 2801544) is not in the 1969 list. The 34 series part numbers didn't start until 1970. I wish I had my 1967 parts book handy.

Edit: Was driving me crazy. Found parts book, 2801544 is listed as "w/426 cu. in. Eng., Hemi, A727B" . So the 2801544 is the correct PN for a 1967 Hemi transmission. Pictures would be helpful to sort out the rest.