1797 REV '97 Large Cent

Learning from the 1851 N17 debacle here is another up for variety attribution confirmation/assistance. I know the coin is pretty ugly. Corrosion, odd toning from a cleaning, the date is half gone, but its old and is my first pre 1800 US coin. I bought it from a LCS, the dealer had simply put 17_ _ on the flip and priced it $45. I guess after ruling out 1799 that was all that mattered. Being that the date is half gone, an obvious first thought would be S-125. I didn't want to repeat my earlier mistake (See 1851 post), I decided to be more thorough. Starting with 1796 rev '97 I ruled out each possibility looking at tons of images. For the '96 date I looked closely at S-100, S-113 and S-114, but ruled them out. I then went to 98 and there really wasn't any that seemed close. What I had left were the following possibilities from 97: S-122, S-125, S-126, S-127, S-131, S-132, S-133, S-139, S-140, S-141.

The coin is so corroded I couldn't tell if it was stemless or not! Had to decipher it using other identifiers.

Anyway, I am at S-125, having ruled out the others after a more in depth analysis. Can an expert out there confirm? What sold me was that despite the poor condition of the reverse, the E in ONE and the T in CENT seem to match up with what one would expect for an S-125. I ruled out S-126 and S-127 because the first 1 in the date is too low compared to the 7. Also, the die clash is present under Liberty's chin.