I used to work in a dental set up for years, but not a dentist. If you had no luck with the ENT, you should ask to be referred to a maxillofacial surgeon. Long standing lesions (2 weeks plus), that show no improvement, or that get worse, within the oral cavity should be biopsied. Especially if you either smoke or drink alcohol regularly.

You're correct, early oral cancer doesn't tend to cause pain (not always the case, though). Everyone is entitled to a second opinion if they have genuine concerns. Having a non healing ulcer is not normal. However, there are other conditions other than cancer that can cause non healing or slow healing patches/ulcers. Such as autoimmune conditions etc.

Weird question, but how are your bowels? I ask because Crohn's etc can present in this way too.