As Harry says the appointment mark is an absolute stone bonker when it comes to a no later than or no earlier than date but even then there is a slight grey area ie when the King passed does anybody really imagine that military tailors just binned any remaining stocks of "By Appt to the King" items even when the Queen ascended to the throne? No of course they didn't and may have even made more before any new appointment was awarded. A royal warrant of appointment would normally be cancelled within 5 years of the death of the grantor (during which time the company should change the marking to "By appointment to the late..." and then a company would have twelve months to alter such markings. So as we see there is some confusion and matters of "form" really.
Jerry mentioned construction and that is probably the best way of dating by comparing to known dated examples. I am not 100% sure but I doubt that minor changes are "legalised" anywhere as long as the item conforms to the approved pattern.
I would caution against placing too much store by badges and buttons as they are very easy to change and as has been already mentioned above these items do tend to change hands and remain in service with new owners as they are private purchase items. As you have seen Matts thread you will have seen my hat from the same maker which is currently still available at around £150 so any officer able to secure a good hat at a much lower price is always going to save the money from his grant I would expect.
You said you are seeking an OR's SD hat to represent the one your Grandfather had (do you know that he had a SD cap rather than a beret? The RA did continue to use them much later than some units but not everyone was issued with these especially during the war). For the benefit of anyone who doesn't know the hat at the top of this thread is an officers pattern which is quite different from an OR type and unlike the OR type is common in service today. Only a couple of units still wear the OR type (Houshold Cav and RAVC are the only ones I can think of and I think RAVC have stopped. My corps wore them in NI in the '70s but not elsewhere after '74).
The GSC button you posted looks like it is on an OR SD cap.
I thought I had posted it elsewhere in the forum but can't find it now so again for anyone who doesn't know here is an OR SD cap;
I hope this helps