Using the two Block G76 to specify an End of Thread Chamfer or via a MTB supplied M code is not going to help the OP at all. All that does is make his issue worse by starting the pullout of the Threading Tool a greater distance back from the specified Z end coordinate. Accordingly, if the OP's aim is to finish with a Full Depth of Thread as close to the face of the shoulder as possible, then having no chamfer specified is his best option.
With regards to setting a Chamfer amount when using the one Block G76 cycle, I think from memory the parameter is number 0109.
Having problem getting the thread close enough to a shoulder,
What is the issue getting close enough to the shoulder? Do you mean that the mating part won't crew right up to the shoulder. In the actual cutting of the Thread, you should be able to safely have the leading edge of the insert go to within 0.002", or less, of the shoulder without issue.
At the start of the Thread, there is a distance where the Lead of the Thread is incorrect due to acceleration. Given your spindle speed of 500 rpm and a lead of 0.04167", the error will be, coincidentally, 0.04167"(one Lead). To avoid this error being part of the start of the Thread, you need to start at least the calculated length (0.04167) away from the end of the Thread in fresh air. You're starting at Z0.2, therefore you have the start covered.
There is also an error in the Lead of the Thread at the finish end of the Thread due to deceleration. For your spindle rpm and Thread Lead, the error distance will be 0.01146". To avoid this error impacting on the length of the Thread that will engage with the matting part, you would have to have a Thread relief of 0.01146, plus the distance of the Thread Form back from the leading edge of the insert.