[BigJJ]

The "Powerized" brand is 1973 forward (the encircled "R" registration mark over the "d" in "Powerized" distinguishes the brand from earlier versions).
The "Genuine" brand over the signature was used only until 1975.
So from these two attributes, the bat can be dated to 1973-1975.
The model A99, length, 35", and weight, 33 ounces, was issued to Aaron all three years, 1973, 1974, and 1975.
Do you know what finish, if any, the bat has? Might be able to further determine when the bat was ordered if finish is known.
So far the specifications and brandings are consistent with what you were told.
I would have PSA or JSA certify not only the autograph but more importantly, the written date.
Also, Aaron should remember the story of the Rogers Hornsby trade for the bat. You actually might be able to have him write a letter, perhaps not in front of a notary, Im cracking up, but you could then get his letter authenticated by PSA or JSA.
In the interim, you may wish to get a -notarized- statement from your cousin. I am not sure what weight this notarized statement would carry, but it is better than no notarized statement. and if PSA or JSA determines that Aaron wrote the "715" and the date on the bat, this in conjunction with your cousin's notarized letter, might have some weight.
Aaron ordered 116 bats in 1974. and 98 in 1973. and 108 in 1975.
Really need the finish to better pinpoint date of the order this bat was in (and number) to better determine odds of it being used in the manner and time described - and/or need Aaron statement, which -is- still possible, can talk to his representative, can get in touch through a company arranging a signing.
Best of luck.