Firstly, there are no leather gaiters installed from factory on any 147/156/GT except the GTA ones, but those are made from GTA seats leather and look a bit different and also the gear lever gaiter is too short for all other cars because the GTA gear levers are shorter.
Secondly, re-stitching is not a very good idea because it's impossible to restitch through the original holes in the leather and those holes will be visible.
Getting custom ones made is probably the answer, but matching leather color and texture is going to be difficult. Also, keep in mind that your original gaiters will be used as templates so you will not be able to use them anymore.
PS. Also, there are 2 colors of TI type seats leather on the 156. The ones from 2002 to late 2003, which came with some sports package, as there was no TI version at the time, are as you describe them, dark grey. From late 2003, when the facelift was introduced along with the TI version, the sets were covered in black leather, much darker and a bit glossier than the previous version.
Not to mention the textile ones from the pre-facelifted interior