In addition to implementing a spam protection based on the mentioned limits (and possibly modding the bot if possible), you could also try to group responses together if commands are executed in rapid succession. For example if a lot of the spam comes from responding with “Queue is currently full”, then you could wait a few seconds with the answer and answer to several people at once (but don’t wait too long or else people may think the bot doesn’t work). You can either only do this when you reach your spam protection, or just do it always so that it reduces chat spam a bit.
Whispering bypasses that spam filter, although it has it’s own spam detection, which can often causes issues for bots if they whisper a lot of people, mostly with similiar messages. I don’t have a lot of experience with that, although it can certainly be useful to reduce chat spam. Also take into account that some people have receiving whispers of people they don’t follow disabled or might not realize that the response came as a whisper.