R library MuMin dredge function not finding data when called from inside a function in parellel mode

Question

I'm trying to call the MuMIN dredge function in parallel mode from inside a function that sets up the data for the model. Even if I pass the data to the clusters with clusterExport, dredge seems to be looking for the data in the global environment. Here is some code with toy data:

library(MuMIn)
library(parallel)
dataGlobal<-data.frame(x=rnorm(20),y=rnorm(20))
cl2<-makeCluster(4)
setDefaultCluster(cl2)

#This works
lm1<-lm(y~x,data=dataGlobal,na.action=na.fail)
clusterExport(cl2,varlist=list("dataGlobal","lm1"),envir = environment())
lm2<-MuMIn::dredge(lm1,cluster=cl2)
lm2

#But not if I put it in a function
func1<-function(dataFunction) {
  lmf1<-lm(y~x,data=dataFunction,na.action=na.fail)
  clusterExport(cl2,varlist=list("dataFunction","lmf1"),envir = environment())
  lmf2<-MuMIn::dredge(lmf1,cluster = cl2)
  lmf2
}
func1(dataGlobal)
# Returns: Error in nobs(global.model) : object 'lmf1' not found

#The function only works if I move the data from the function to the global environment
func2<-function(dataFunction) {
  lmf1<-lm(y~x,data=dataFunction,na.action=na.fail)
  assign("lmf1",lmf1,envir=globalenv())
  assign("dataFunction",dataFunction,envir=globalenv())
  clusterExport(cl2,varlist=list("dataFunction","lmf1"),envir = environment())
  lmf2<-MuMIn::dredge(lmf1,cluster = cl2)
  lmf2
}
func2(dataGlobal)
#works

How can I give the data from the function's environment to dredge in the clusters without copying it to the global environment? Thanks