Take a look at spring Triticale.  I would think it would be a better choice than winter rye.  Whether spring triticale will be better than spring oats for straw.... I don't know.   Wolf River Valley seeds has one spring triticale in the seed catalog.  I don't know if any other companies have any in their product line-up.

I found this link on spring triticale for straw.  I thought the comments were interesting.

The other thought that crossed my mind is spring barley.  I don't know if it will yield better or worse than spring oats.  I think oats would give more straw.  However, the texture of barley straw would be different. I would ask the farmer which he would prefer - oat straw or barley straw.  Like the spring triticale, you would have to do some digging to find spring barley varieties in your area.

ForageSeeds.com has both spring triticale and spring barley