At one point the AMA did lobby Congress to limit the number of doctors but they reversed their position on that issue long ago.
New York accounts for nearly half of all state Medicaid GME funding nationally, with NY state Medicaid GME alone reaching ~$1.8 billion of the $4.4 billion total GME spending in NY in 2012 (federal + state + private).[1]
And is New York better off? Do these claims about GME hold up there? Don't blame AMA or Congress, blame your dominant state political party. Congress should probably require matching for GME which would completely cut off funding for most states. We can already read the headlines.
If you actually knew about this before I mentioned it please let me know, but I think you likely didn't, even though you've obviously spent time researching this important topic. I am actually more irritated how little "people in the know" actually know. It's why I despise outlets like NPR who spread propaganda (agitprop mostly) and refuse to report relevant info and the damage it has caused to America's intelligentsia. Defund NPR and friends, they are the root cause of this mess.