This depends on how much your friend would like to change himself for his social life.

I'd not expect neurotypicals to be acceptant of stilted speech because it is a deviant behaviour that I am conscious of. I do this anyway like how you describe your friend, a) I'm self-conscious and anxious and b) it's a habit. It is possible, however, for me to tune down to internet-speech mode but that occurs only when I am with people I am extremely intimate with and can feel relaxed with. Once I'm conscious of my speech (like when I'm answering this post) i resort back to formal tones.

There are two obvious options for your friend rn. he either keeps his speech behaviour and receives negative sanctions from his social circle, or suppress it (this takes tons of efforts especially if he's on the spectrum) and improve his social wellbeing. Both of them will incite anxiety along the way and I personally would retain what I have right now, partially due to inertia and partially because I avoid social interactions anyway. It's up to your friend if he really wants to change his stilted speech or not.

It's great how you'd like to understand and help your friend, anyway.

I hope this helps.