Nige, can I put standard width tracks on the machine ?
A clarification. The track link group (aka chain or rail as it's often called in the US) is the same.
The shoes are bolted on to the links. So you can put whatever width of shoes you like on any link so long as the bolt holes line up.
Your tractor S/N ALY02331 (BMA29824 is the engine S/N) was originally built with Cat's SystemOne undercarriage with 34"-wide track shoes. The track that is split and on the ground is definitely S1.
I'm not sure if the idlers on it today are S1, maybe someone can say for sure. They may be very early ones but the illustration in the Parts Manual does not show them like your photo. Can you see "Cat ©" and maybe a Part Number marked on them anywhere..?
Track shoes for your specific D6N (which was built as an LGP machine with wide shoes) are available in 28", 33", & 34" wide. Standard tractors also had 22" and 24"-wide shoe options. So in extremis you could go from the 34"-wide shoes that are on the tractor now right down to 22"-wide shoes.
None of the photos show the track rollers. Again S1 and HD are different.
One thing I can say for sure is that it's not recommended to mix S1 undercarriage parts with Heavy Duty undercarriage parts.
You say that you are in for a complete new undercarriage anyway, so you'll have to make the decision which type you go for.
If you go for S1, Cat is pretty much your only source of supply.
If you go for Heavy Duty then it opens your choices to pretty much every aftermarket undercarriage supplier out there in addition to Cat.
There is documentation available to make the conversion from S1 to HD undercarriage. You probably need that first so that you can see exactly what you would have to buy, modify, etc, etc, in order to correctly change from S1 to HD and not screw anything up if you go that way.
Last parting thought. You probably want to check both the equalizer bar pins/bearings and the pivot shafts to make sure nothing's worn out in those areas before you start to think about putting U/C on it. An alignment issue could cost you big style in premature wear of the new U/C.