Just try and schedule your anesthesia rotation for early fourth year (June or July). This should be just enough time to ask for a LoR and get it in your ERAS before September 15th (when programs receive applications). You can also try and schedule a sub-I in the July-August range and get a LoR from that as well. You should be fine with just 1 letter from an anesthesiologist (given other parts of app are sufficient), but more wouldn't hurt I suppose.
As mentioned above, when you're on your surgery rotation, try and sneak into the OR before surgery starts and hang out with anesthesia. I was able to do this on most cases. They're usually happy to let you mask ventilate, intubate, set everything up (given that they don't have their own student). Besides, the attending surgeon doesn't show up until the patient is prepped/draped anyway, so you have a good 10 minutes to chill with anesthesia at that time.