1982 Standard Specs
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The shackles don't need to be factory. but under the ADR's extended shackles are not allowed. So just buy/make some stock length shackles as there simply is no way around it and they can't approve longer shackles.
Track is measured from the centre of tyre to centre of tyre, so its the wheels not the tyres that need to be assessed. (ie what's the spec of your rims?). Although you'd like to think he'd sign off on a small 31" tyre - some can be a dicks about it. The stock tyre was 235/75R15 ie 733mm tall, then a 31" tyre is 787mm = 54mm. The rules specify 50mm...sucks I know but IMHO it may be just easier/cheaper to grab a set of Zuki rims with 235/75r15 tyres and get it passed on those then just swap the existing one back on afterwards.
Whilst there are engineers that would probably do tests to pass larger tyres, to be honest you don't want that because it can be way more expensive for really very little gain.
Swap it to stock it's not much work/cost and then your done. just my 2cents....