Your points about the annulment are good, but it is pretendland, so it's not that much of a stretch, especially given how the show needs to tidy things up quickly. The book could take the same deus ex annulment direction but flesh it out so much more that it would actually be convincing. The show doesn't have this luxury.

As for where the Kings Guard having no business being with Lyanna, I think you're way off. Some of the Kings Guard were with Aerys (we know at least Jaime was), some may have been with Elia and her children, others on Dragonstone with the Queen, and that still easily leaves two or three to be guarding/under the command of Rhaegar. If we accept the annulment, it is perfectly plausible that his Kingsguard would see it as their duty to both follow a direct command from their prince, as well as guard Lyanna, who's now a princess and next in line to be queen, as well as their potential future king.