A therapist isn't anyone's emergency-now friend. Like doctors, lawyers, CPAs and other professionals they have lots of appointments and the needs of the practice they work in to fulfill. That's exactly why there are appointments: it's not burger king and if you get your way then the questions are: "do my concerns need to bump another appointment to some other time?" and "to anyone but me is this an emergency?"
If it is an emergency you should not under any circumstances wait for the next morning to call your therapist. Instead call 9-1-1, go to the nearest emergency room or contact your local mental health helpline.
If it's not an emergency, discuss the matter at your next scheduled appointment. Appointments are made according to the level of acuteness of the patient's state-of-mind, behavior and emotional stability: more frequently for the acute patients, less frequently for the less acute patients.
Judging by what you've said you fall into that not acute problems patient group. Sounds as if you made monthly appointments.
If this was an issue that's been brewing then you should have discussed it at your last appointment. If it's something totally new and totally unforeseen then you might evaluate just how much of an emergency it is.
You should have had your phone call returned if the therapist said to you they would call. The fact they actually said they'd call you the next day seems unusual to me. Normally you'd get a message telling you that they'd return calls as soon as they may, but would never give anything remotely like a guarantee for a certain time or day. But people have different SOPs.
I've found though that my failure to plan or do a thing properly did not constitute an emergency on someone else's part.
If you already have your letters then you shouldn't be too concerned about "recriminations." If your therapist is as good and recognized as you say they will not do anything to prevent your SRS to go as scheduled. That would be unethical and not very good for the reputation either.