Straw type mulch takes more maturity than you can achieve by April.
Flax makes a very tough straw that they make linnen out of. It will stay intact over the winter as a straw mulch if planted thickly from my experience last winter. If you can plant it as an under crop for tall crops and then it can continue to grow after the crop harvest until flattened by snow you will have a straw mulch when the snow melts.
I am in zone 7 so I usually get one snow event in december and another in January and the snow only lasts a day or two. but the black flax that I bought in the bulk bins did the job and now weeds came up in the two long strips that I planted it.