People with no intrinsic factor do indeed absorb orally...
this is done PASSIVELY with large doses of 1 to 5 mg a day.

There are many studies to show this now works orally when taken daily on an empty stomach.

I would get the DNA testing for MTHFR mutations which are very common also to see if you require methylcobalamin. Most injections are cyano type and have to be methylated to work in the body. Otherwise you don't get the benefit of cyano injection or oral.
It will show up floating in your blood tests, but it will not work in tissues if you have the mutation.

Vitamin B12 Deficiency - American Family Physician

This link is for doctors education, but lay people can understand it too as it is written very well.

You can choose to do what you want. But do research showing oral will work, to save you the invasiveness of injections, and the use of the right type of B12 so it will actually work once injected.

I am sorry your doctor remains uninformed, but you can give him that article to explain the newer aspects of B12 therapy.