Is it the case that the invocations restricted to a specific number, such as "Subhan Allah wa bihamdihi (Glorified is Allah and with His praise) one hundred times," are to be recited only by this number throughout the day, and anything exceeding it is to be recited without a specific number, or is it permissible to repeat this number multiple times a day?

What you mentioned, that adhering to a specific number for dhikr is an innovation (bid'ah), is not entirely correct. Rather, it becomes an innovation if it mimics what is legislated, meaning if one adopts it as a regular Sunnah and believes in its legislated nature in a way not brought forth by the Sharia. As for merely performing dhikr a specific number of times, it is good and falls under the command to remember Allah frequently. So, if you perform the prescribed dhikr, it is permissible to repeat it without a specific number, or with a specific number, and both are good according to the aforementioned guideline.