Though I hate to say this, I don't think that will help much anyway. The idea of a slow mode might help, but having two spectator tabs open is more of a headache for the player, especially if it is someone who doesn't get a lot of spectators, they get quite a few from the song they are playing and people are hl them in both. With two, the spectators don't know what the others are saying and will probably cause more problems for the player.
I know for me I have literally stopped playing just from people spamming Dragon (i.e. Blue Dragon hl spam) and ds (i.e. #modhelp using it for a short way to say distance snap) because it annoys me that much and the hl spam makes me miss, but it doesn't happen often enough for me to disable the notifications because I have people occasionally message me when I am playing or when I have the game running but minimized.
Restricting it to friends would be helpful if you could do it after it hits like 10 spectators so that reduces spam there. For chatting, you can go down the road of having a tab dedicated for the spectators themselves that the player they are spectating cant see so - therefore - cant see the spam. You wont be able to really reduce spam though in #spectator because - when someone gets a #1 - people are going to say "OOOOOOOMMMMMMGGGGGGGGGG" "HOW DID YOU DO THAT" "PLAY THIS" "MARRY ME" (I have seen this one more than once) "ADD <insert mod here>" regardless of whether or not they are supporter. I have even seen ExGon with like 12 spectators have his #spectator tab blow up just because he got #1 on a song no one cared about. All but one or two of them were supporters.
It is a good idea to want to reduce spam, but you really can't fix that until people themselves want to stop spamming or get silenced from it.