A theraputic school is not an appropriate placement for a child who just made a garden variety mistake and who does not suffer from mental health issues. Half the day at theraputic schools is devoted entirely to therapy. However, for kids who struggle significantly with anxiety, depression, trauma or attachment issues, they can be transformational.
A consultant can be a great help when you are looking for a second chance as they have relationships at the schools and can have the hard conversations with the new school that are awkward or uncomfortable for a parent, and they will know exactly who has space for next year and be able to give you an honest assessment of your chances based on conversations with the AOs who trust them.
Many (most? all?) the students at our local therapeutic BS have substance abuse issues or boundary type issues, not what are commonly thought of as mental health issues.
I just threw that out there in case the shoe fits.
My nephew attended a small private day school that probably had 3-4 kids join his class over the years after they had been expelled from BS. By all accounts, they did well - one gave a speech at commencement about turning mistakes into opportunities! If there are any similar schools around you, @cowanddog , it might not be a bad place to start. It’s also worth asking your kid what they think - what led to making that mistake, what kind of environment they would do best in, what kind of support they need to not make similar mistakes.