I don't have any written timelines of a 'West vs East' long-term standoff, but on the necessary factors for the West surviving (as it does in my Alternative History of Rome scenario) the main ones are the continued occupation of Marcomannia / Bohemia and Moravia after 180 plus the ditto of Dacia after the real life presumed evacuation in the 260s. In both cases I have the West occupying them and the local Germans enrolled into the Empire's armies - hence my stronger showing for the Empire in the mid-C3rd in my series of articles. If we carry this scenario into the later C4th we may have the Goths heading there not into the lower Danube region as they flee across Wallachia from the Huns in the 370s - though the West could block up the Carpathian passes to stop them, easier than the OTL East holding the Danube against the Goths.
A German 'wave' of refugees overunning either Dacia or Marcomannia , or both, is more likely if there is a huge migration of tribes fleeing the Huns under Attila, ie in the 430s and 440s; but if so, the refugees are heading into the modern Czech Republic and southern Germany not over the Rhine - so Rome keeps the lands West of the Rhine and the 'Aetius and the Germans defeat Attila' conflict is East, not West of the Rhine. Then Attila dies and the German vassals of his empire revolt as in OTL 454 - and if Aetius is still alive after 454 he can enrol them as allies of the Roman army and dominate central Europe with an argument of 'if you don't join us the Huns will come back, if you do join us we can keep them on the defensive'. That way the West not the East has the stronger army in the mid-lateC5th - assuming that there have been fewer inter-Roman civil wars, eg Theodosius I living after 395 or Stilicho keeping control of the West after 408, then Constantius III not dying in 421 and Aetius getting rid of the useless Valentinian III in 454 not vice versa. This is the main argument in my 2011 Pen and Sword study , 'If Rome Had Survived' - second edition coming out shortly - and in my narrative books of 'continuing Roman history'.
As for an equally balanced East and West in the C6th to C7th and no eastern reconquest in the 530s - the above situation, plus the aggressive and expansionist Justinian not being Emperor - which may well follow if his uncle and predecessor Justin, whose deputy he was, is not elected Emperor in July 518 when Anastasius dies. Possibly A's nephew Hypatius is more competent and is elected then, not passed over; or the rebel general Vitalian , semi-reconciled to the govt by 518, stages a coup.
To avoid or limit the Arab conquests - butterfly away the exhausting Roman vs Persian wars after 602, so the Empire has more men and money when the Arab armies arrive in the 630s and the region is not exhausted by decades of war and a Persian occupation of Syria, Palestine and Egypt. Possible if Maurice is not overthrown in 602, which started a civil war and Persian attacks - which would be possible if M was not unpopular with the Balkan army. For that, try a surviving Western state still running Dacia - it can take the Avars in the rear and help Maurice defeat them quicker. Or the aggressive Persian Great King Chosroes/ Khusraw II is not restored to power (by M) in 590.