Randomizing 1s and 0s by groups while specifiying proportion of 1 and 0 within groups

First, I want to create a column that randomize 1s and 0s by group while maintaining the same proportion of 1s and 0s in another column.

Second, I want to repeat the above procedure many times (say 1000) and calculate the expected value.

Let me clarify with hypothetical data.

library(data.table) 

district <- c(1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3)                                       
village <- c(1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,7)                              
status <- c(1,0,1,0, 1,1,1,0,0,1,1,1,1,0,0,0) 

datei <- data.table(district, village, status) 

What I want to do is I want to create a column that randomize 1s and 0s within a district while maintaining the same proportion of 1s and 0s in status; the proportions of 1:0 are 2:2, 3:2 and 4:3 in district 1, 2 and 3 respectively.

Second, I also want to repeat this randomization many times (say 1000 times) and calculate the expected value for each row.

I know how to randomize 1s and 0s based on district.

datei[, random_status := sample(c(1,0), .N, replace=TRUE), keyby = district]

However, I do not know how to have the same proportion of 1s and 0s as in status and how to repeat and calculate the expected values for each row.

Many thanks.