Have you looked on local county council sites for teaching jobs that aren't school-based? They usually come under the "normal" job search, so along with other council roles. I'm a peripatetic Teacher of Deaf Children and Young People. I visit children in schools who have a hearing loss, advise staff on reasonable adjustments, do language interventions 1:1, lead INSET sessions, attend annual reviews etc.
I have no displays to do, don't have to be at school for 8am, can do online meetings and PPA from home, only ever work with 1 student at a time, no big loads of marking, no sitting in assemblies, no playground duty, no data-driven performance management etc. A couple of days a week my first visit of the day is 9:30 so I can do the school run.
I do have to write reports, do paperwork, language assessments, email schools, ring parents etc. but it comes with far, far less pressures.
And the best thing? UPS3, plus SEN points, Burgundy Book and all the school holidays.
I had no SEN training before starting the job and work paid for me to do my mandatory qualification.
There are other advisory teachers, not just ToDs.