(Making my comment into an official answer.)
@StephanKolassa commented here explaining his concern with your question. The close reason is "In the meantime, I am voting to close as unclear". Three subsequent users have voted to close for the same reason, two of whom before you added the code, and one of whom after.
I don't see that Stephan has revisited since his comments, but it's hard for me to tell. If it is closed & he thinks it has become answerable, I can reopen--just flag it.
Stephan revisted the thread and commented:
Thanks for adding the code; I have retracted my VTC. I have a suspicion and hope to find time later today to follow up on it. (Note that stepwise and approximation are only relevant for the first model, where I indeed get the same AIC as you do.)
I have voted to leave open in the close vote queue. My vote should be binding, meaning that it will no longer show up in the queue for others to vote to close on. You should be safe from closing now. Again, if it does close, just flag it and I can reopen it easily.