I span extremely slow for the longest time ever (250-300) and still spin pretty slow (350 avg now) but what made me improve was simply playing more and not caring about spinners. As long as you don't get a 100 or worse on a spinner then it's fine.
Always prioritize technique and form over speed, even if you spin a little slower, make sure you are spinning the same size circle every time, and try to make it pretty small. Over time you will get faster, but just keep in mind spin speed really isn't important. There is rarely a case where you even need to spin 300+, bonus points only really matter for multiplayer or trying to get on top 50 leaderboards of easier songs.