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3 turns of thread engagement
You should be aiming for 10 turns (8mm on an M5 skewer). That takes you back down to the 117mm, i.e. 100 OLN and 8.5mm thick fork ends. Halo XL Allen key skewers are listed as 122mm max, so if your fork ends are 6mm or less thick they should work, in a limited sense. It's worth bearing in mind that Allen key skewers are even worse than QR skewers in terms of the disc brake wheel ejection issue referred to above, whereas track nuts are several times better than even a Shimano closed cam skewer.
I checked the two within arm's reach (Shimano enclosed cam and Miche X-Light) and they're both about 123 mm with the cam closed and a minimum 3 turns of thread engagement.
I reckon there's enough variation in front skewers that a rummage through an LBS parts bin might find one that will work.