Apologies for the delayed reply, been busy in the so-called real world :-).
Here it is...
1) Install Silent 3ditor (aka S3ditor), available at
https://silent-3ditor.software.informer.com/0.9/
2) Using S3ditor, navigate to SH3/data/Library/Torpedo.sim (where SH3 is whatever you've decided to call your install). Open 'er up.
3) Open 20: amun_Torpedo, which should in turn lead you to 21: amun_Torpedo. This is what you're looking for.
4) Inside 21: amun_Torpedo, you should fine a subheading of Speeds [1]. Click on this to reveal a further subheading simply called [0]...
5)...clicking on this, in turn, reveals yet further subheadings of speed and - at last! - range. Click on range, and the "Property details" box at the bottom should have an editable field which, by default, will read 5000.0. Simply edit this to whatever you desire - Wikipedia says the T III's range was actually 7500m, so that's what I went with. Once done, save your changes.
Almost done...
6) Go to SH3/data/Menu/en_menu (or fr_ or de_ equivalent if not playing in English) and find the lines relating to the T III - line 625 in my install. Simply change the part that says "5km" to "7.5km" to have the in-game description match your changes.
Hey presto!
NB - doing this has just made me realised that I didn't similarly adjust the T III FaT and LuT torp ranges to match; if you're so inclined, the amun_Torpedo files you're looking for are 10/11 and 14/15 respectively. en_menu descriptions at 626 and 630.
Hope this works for you; if not, one of the kind people above may be able to help out :-) happy hunting!