Per Mahler, there is only one reported example of an October 1, 1862 cancel on document. More are possible, just not reported to him.
A quick search on my site shows 21 stamps with October 1862 cancels, of which 17 are on document. My earliest are October 2, two examples dated October 4, and an October 6. The penmanship on the October 2 document is a bit indeterminate with respect to the date on the stamp itself, but we can date it via the check number (several years back there was an eBay
seller that would regularly sell off checks from T.P. Howell & Co., all from 1862 and early 1863, and once I recognized them, I patiently waited for and purchased every lot that came up, so I have a whole sequence of check numbers and date data from that particular company).
I have an R53b dated October 1, 1862, but that has to be backdated, as according to the Boston Book, the 40-cent Inland Exchange wasn't first delivered until December 4, 1862.
No, an October 1862 calendar (and to a certain extent November as well) present a daunting challenge.