Are we sure Madoka isn't getting slightly more powerful with each time loop? She originally lost on the first Walpurgis Night.
If Madoka can vaguely recall what happens from the previous time loops, then maybe she can draw power from her other selves as well. Then she could become a Puella Magi without contracting with the current Kyubey and win on Walpurgis without exhausting her magic power and becoming a Witch.
Remember that in a magazine scan, we see both a normal Madoka and a Puella Magi Madoka together. The same goes for the opening sequence. We see a spiritual Madoka embracing the normal Madoka, transforming her into a Puella Magi without any trace of a Soul Gem. Maybe it's possible for Madoka to bypass Kyubey's system after all.
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