And again, the same basic tenets still remain in place:
Those are not basic tenets, they are the general setting but you lack very important details or you miss the entire point that this type of histry is NOT made by grand narratives or general settings, it's made from a multitude of factors causally linked to one another, if you move just one it's going to make a mess of everything. Butterflying away doesn't mean you cannot come up with a timeline that still has Islam in it but it would be awfully coincidental if it's exactly as OTL Islam is considering 3 entire centuries of religious history in Eastern Rome is changed.
If it actually existed at the time we have no reason to believe it would inevitably become as important as IOTL.
Roman successor states and Persia duking it out with each other and themselves in civil war - check.
Islam or rather proto-Islam was not born over centuries of people living near this conflict, it was born within 1-2 generations under a very specific war during the lifetime of a prophetical figure that had a specific backstory, lived in a rather specific geopolitical and social situation which wouldn't exist as such with butterflies.
No power wanting to invade Arabia other than some coastal cities for trade - check.
Except through their vassals and through their commercial control I'd estimate around half of the Arabian population in the late 6th century lived under direct or indirect Roman-Iranian control, especially considering Yemen.
I would like to ask how does this PoD exactly change this? The Arabian tribes in the interior who had no access to the most lucrative part of the trade routes, have basically the same life cut out for them.
Is Islam just a generic chemical result you get out of mixing those ingredients? Because that's how you are treating it, human ideas cannot be treated as such.
Sigh, but it's becoming pretty obvious that you're not understanding the point here i guess. A religion like Islam or Islam itself was largely inevitable in Arabia. The arabian polytheistic belief was so loose it isn't funny. This in itself led to several wars, and basic principles of Islam derived itself from the Jews and the Maronite Christians in Nabatea and Petra. In fact proto-Islamic religions like ones Ma'in started but failed. These proto-religions were amalgamated into Islam alongside the 'revelations' that Muhammad had. Something like Islam or Islam itself just founded by some other king which is successful this time would come to being in an area that wasn't affected by Rome for the most part.
And why would it be successful in a world where there was no unified Roman Christianity? Why wouldn't they, for example, convert to Judaism or Christianity? If by Islam you mean the specific religion then you need to show how are the important elements of the religion are going to be inevitable with actual arguments, not just showing that the basic ingredients are there, which they really aren't given that if Rome collapses before Christianity is there the connection between Christianity and Romanity is weaker and Christianity has less of a chance at establishing itself even in the East.
If by Islam you mean very vaguely a monotheistic religion, even Christianity or Judaism, followed by Arabs then that's a different argument entirely.