I'm sorry you you guys haven't found anything that has helped. Voice disorders can be a complicated to identify the origin. Extreme stress, PTSD, anxiety etc. can cause voice disorders in some cases and people find that the onset is sudden.
While I respect ENT and other physicians expertise and training they typically are not well versed in the treatment and therapy SLPs provide and not just voice related just in general. For voice disorders like yours its important to see an SLP that specializes in voice disorders because while the average SLP may be able to do voice therapy basics they may not have access or knowledge to all the modalities an treatment techniques available. Your ENT is likely speaking in regards to fixing or improving your voice like the Botox did when you were able to get it done. Therapy is highly dependent on the individual, an SLP won't fix/cure a voice disorder but they will work with you on techniques and modalities to improve communication which might not necessarily be verbal/voiced. Treatment may focus on alternative ways to communicate to help maintain an individual's quality of life and participation in socialization. It's important when meeting with an SLP for the fist time is to have clear expectations of the goal of the therapy. Another aspect of going to an SLP is the time they are able to spend on really educating patients. Physicians just don't have the time to spend providing in depth training due to the way the medical system works. There techniques like vocal hygiene that can help with comfort and taking care of you voice. Depending on where you live there may be a clinic that specializes in voice disorders. I live in Oregon and there is a large university hospital here that has a state of the art voice and swallowing institute where ENTs, GI's, and SLPs all work in the same clinic allowing them to work together and consult each other. Not everyone may have access to something like this but I recommend it to many patients who need specialized treatment.