For normal time/mileage servicing the check list is in the back of the hand book so there is no excuse for any garage to miss out anything. Regular servicing on a Supra is no more difficult than any other car. I have always had mine serviced at Toyota, so I know that the car has the correct service at the correct time using the correct fluids and parts. Also, if there is an issue, and there hasn't been in 7 years, I'm dealing with a major car manufacturer, not some one man band.
Phoenix seem to have a very good reputation on here, but other so called 'Supra Specialists', (Turbofit, Max GT and Mkiv Store spring to mind), have caused no end of problems and damage to members cars.
Your choice