Did your doctor ever bother to do a c-peptide test? That would be a good measurement of how much insulin your pancreas still produces. Make sure you do not fast before the test as it can your end false low results.
Honestly, I have the same question you do: what are we missing here? It's almost as if your doctor doesn't know what type of diabetes you have so he's just classifying it as type 2.... As I've mentioned on this forum before, that's really what "Type 2" is. It's not a specific type of diabetes, but rather the group of unclassified diabetes.
Personally, I would NOT accept the recommended treatment you were given or even the answers you received. Type 1.5/LADA if misdiagnosed as type 2 can be very dangerous as the chances of you needing artificial insulin are all but inevitable, but the chances of you getting it prescribed are slim.
By some standards, I may have type 1.5/LADA as I'm still producing some natural insulin more than 14 months after the first signs I had diabetes. Fortunately, my doctors have never once even brought up the T1.5 term and always classified me as type 1.
Of note: I live in the US so there was never a possible "conflict of interest" for a doctor to try to save costs and avoid prescribing insulin.
Within 3 weeks of my diagnosis, I was on Levemir, Novolog/Novorapid, a Dexcom G5 CGM, and an Accu-Chek Aviva Expert.
My point is, if you're not comfortable with the answers you're receiving keep pursuing this. I know I would if I were in your shoes (and I was last year).