On an SG1 and an SG3 here, the right margin stop locks the printing keys as expected at x characters after the bell but not the spacebar nor tab, which both ring the bell and then blow right past the margin stop. Additionally, when the End-Of-Line lock stops the printing keys, I can continue spacing past the margin and then after about three spaces on the SG1 and about eight on the SG3 the printing keys are again active.

On some typewriters, there is a feature called the End Of Line Lock which has this effect on the key action. Its purpose is to prevent inadvertent typing when the carriage is at the right margin. It is a bar across the width that prevents the links from going through their whole range. When that lock is stuck has the effect you are seeing at every position. Now, in this case it may not be stuck by dirt or bent parts but instead by the lack of its return spring. So, inspect the action until you understand how it works on this tw (It's triggered by a part on the carriage hitting the right margin stop, which causes that bar to move into position to block the type linkages.) and look for a place where a return spring might be missing or disconnected. Fix that. This might not be your actual problem but it is the most likely.

Likely the key lockout isn't resetting like it's supposed to upon carriage return - the little part you mentioned. Cleaning and light oil on the friction and pivot points of that and the margin stop assembly usually can get things moving again. That's the most common issue I see in Royal Standards.