WI: The Second Barons War End in Victory for Simon de Montfort

As the title says, what if the Second Barons War had ended in triumph for Montfort and the Baronial cause, with the provisions of Oxford ending up becoming something of a second, far more encompassing, Magna Carta?

As a more specific POD, after Henry III of England had fleed the field of Lewes in defeat and sought refuge in a priory, the sources we have described his armors as damaged by the fighting, showing that it was something of a narrow escape. Therefore, we can easily imagine Henry being captured by Simon's forces instead of simply having to negociate a settlement from a position of clear weakness like in OTL, significantly reinforcing the, already quite solid at this point, barronial hand.
 
3 options:
1) nothing much changes in the long term and royal versus noble absolutism heads towards parliamentary sovereignty as both seek popular support
2) noble supremacy. This may lead to a more noble republican future and its various outcomes
3) a later king uses popular support to install himself as absolute monarch. This leads to similar various outcomes
 
3 options:
1) nothing much changes in the long term and royal versus noble absolutism heads towards parliamentary sovereignty as both seek popular support
2) noble supremacy. This may lead to a more noble republican future and its various outcomes
3) a later king uses popular support to install himself as absolute monarch. This leads to similar various outcomes
I am honestly not sure about 1) and 2), as both the provisions of Oxford and Westminster do show some restrictions on not just royal but also barronal freedom of actions, and some actions and writings by Montfort tend to indicate that he was a true believer in that regard.

Now, don't get me wrong: the guy wasn't an early days democrat or something like that but I feel that depicting him and his cause as a mere vehicule to replace royal supremacy by barronial one isn't quite fair either.
 
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