First of all: It's not going to rain this year. Period.
Second: The straw is meant to absorb some of the water and mix with the mud to become a more firm surface. The geotextile that was used for runways will just let all the water through and be stomped into the ground. I'm not sure that'll work.
My suggestion still is to get the military involved and have them lay temporary roads - or bridges if it gets really bad
.