If we assume that Edward still dies in approx. 1307, then the succession is very complex indeed. There are many options:
1) Edward's eldest daughter, Eleanor, died in 1298, so her heir was her son, Edward I, Count of Bar. Sadly, he wasn't even a teenager, and was foreign.
2) Edward's second daughter, Joan of Acre, died a few months before her father, but there's no reason she couldn't survive and become Matilda II: Electric Boogaloo. She had many children, including Gilbert de Clare, 7th Earl of Hereford, who was on the cusp of manhood, as they say in bad historical fiction novels. Her corner would be fought by her second husband, Ralph de Monthermer, who was a bit of an upstart but seems to have been competent. He might end up as King jure uxoris, in which case there are going to be some firm and frank discussions between his family and the de Clares descended from Joan's first marriage.
3) The other daughters of Edward I to have issue were Margaret and Elizabeth. If either of them is the eldest living sister in c.1307, they might have a go at claiming the throne. Margaret was married (unhappily) to the Duke of Brabant and had a 7-year-old son, while Elizabeth was married to the foppish Earl of Hereford (who would be in charge of the political and military side, obviously) and was popping out babies at an alarmingly fair clip. The only likely Matilda-clones are 1 and 2, though.
4) The Stephen of this civil war would be Thomas, 2nd Earl of Lancaster, and frankly, its hard to see how any opposition to him would last long. He was the largest landowner in the country, he was popular with the barons, and his younger brother had his back. As well as being heir by the law of 'might is right' he was also heir by Salic Law, which hadn't yet been explicitly rejected at any point in England, and could theoretically become the new modus operandi. Indeed, Edward III eventually came out in favour of it, but that was at a point when it was unlikely that the Plantagenets would die out - which is a possibility at this point.