A minor correction to your characterization of the Time of Troubles: Ao didn't make the gods mortal, he simply locked them into their avatar forms for the duration of the event. They were only present on Faerun as their avatars, and could not act in Realmspace (the crystal sphere containing Toril and other associated worlds) outside that avatar.
To quote from Faiths and Avatars (2e), page 15:
During the Time of Troubles, the powers of the Realms were forced to either place all of their divine power in one mortal avatar or, if they exist on multiple planes, were forced to create avatars upon whose existence their entire future divine connections to the Realms were staked. Since the powers of the Realms were forced to stake so much on their avatars, these avatars were acutely vulnerable. While the death of an avatar did not mean the death of the power (Bane and Bhaal, at least, went through multiple avatars in succession before finally dying), powers could only maintain themselves in one avatar form and could not connect with their homes and power bases in the Outer Planes (if they had them).
It goes on to clarify that even during the Time of Troubles, any divine deaths were still at the hands of other gods, even if only by technicality. Bhaal's death by Cyric was via the sword Godsbane, itself an avatar of Mask; Myrkul's death by Midnight was while Midnight held some of Mystra's divine essence; Mystra's death was by Helm while trying to get to her home plane via the Infinite Staircase; Bane's death was via a combination of Mystra's remaining divine essence summoned by Elminster and Torm finishing him off in Tantras.
But as for your main question, that quote addresses that: beings like Lolth and Gruumsh were just fine outside Realmspace, but within Realmspace all their influence was limited to a single avatar, and if that avatar was destroyed and they couldn't muster another, all their connections to Realmspace would be severed and they could no longer act as deities within that sphere.
For some more information to help, Planescape's On Hallowed Ground goes into what exactly overpowers can do above and beyond other deities, and clarifies that their influence is limited only to their own crystal sphere. From page 160 of that work:
The poor prime gods don't always have the final say on their own worlds either. Some of the toughest bow to a still higher deity, an overpower who watches out for the entire crystal sphere. Each overpower is concerned with only a single sphere, and has no influence outside that realm. Chant is they've tied all their strength to maintaining the one sphere; perhaps they're simply its spirit made real.
Also, for what it's worth, FR's unique presentation of the planes only dates back to 3e; before that, it used the Great Ring the same as every other D&D setting. There were even a few Forgotten Realms works that directly crossed over with the general D&D multiverse in 2e, including the adventure For Duty & Deity, the Ravenloft novel Vampire of the Mists, the Forgotten Realms/Dragonlance/Planescape novel crossover trilogy The Lost Gods, and the classic (if not technically canon) Dragon column "The Wizards Three" where Elminster, Mordenkainen, and Dalamar hung out and made things difficult for Ed Greenwood.