Given their Tannenbaum-level cap hell, if they hope to re-sign Burton, they almost have to cut Celek to gain his $4M in cap space. They certainly can't cut Ertz and his $10.6M cap hit, because it would actually put them about $2.6M deeper into the hole against the cap - which is already a $9.1M red number even before including Michael Bennett. Furthermore, Ertz's contract (above even Gronk-level) has four years left on it, which may make an extension-restructuring difficult.
The Eagles have only five days left to get under the cap. I'm guessing that they cut Celek ($4M), Torrey Smith ($5M) and Chris Long ($2M), and try to unload Vinny Curry ($11M) via a trade. They'll still need to restructure players like Graham ($7M), Jenkins ($10.1M) and Lane Johnson ($12.5M), just to get be able to re-sign Burton, maybe Bradham, and still have some breathing room.