What if the reverse happened - rather than march on Rome, have Aegidius declare Ricimer a usurper, and call for a Senate in Gaul to declare a new Emperor. His armies may just declare him, and then offer the lands to the Burgundians in exchange for their allegiance - essentially an early version of a March. (You could do the same with the Visigoths if you put them closer to the Pennines).
Then the "Dominion of Soissons" can be a renegade realm until the Romans lose Italy, or until Aegidius is recognised as Western Roman Emperor, or least Kaisar, or Dominator in the West.
In fact, Aegidus, rather than trying to march, can also try and convince Marcellinus in Dalmatia to swear for the Eastern Emperor.
If all that works, and you have The Western Empire ruled from Soissons, with a Burgundian March and a Visigothic March, Aegidius COULD reform Gaul, and work to reunite Spain with Gaul. Heck, depending on circumstances, if Soissons and the Burgundians agree to occupy the western front, the ERE could make a move on Italy, giving Liguria to Soissons.
You could legitimately have a situation there the ERE controls Italy, Africa, and Spain - with Soissons being organised around Gaul and Germanic Marches - which a peaceful relationship between the ERE and Soissons leaves a Rhine border that can be easily pushed eastward - with the WRE becoming more Northern and Germanic, and the ERE being more Southern and Mediterranean.