R: Moving average length of time between two dates

I have a dataset of observations with start and end dates. I would like to calculate the moving average difference between the start and end dates.

I've included an example dataset below.

require(dplyr)
df <- data.frame(id=c(1,2,3), 
                 start=c("2019-01-01","2019-01-10", "2019-01-05"),
                 end=c("2019-02-01", "2019-01-15", "2019-01-10"))
df[,c("start", "end")] <- lapply(df[,c("start", "end")], as.Date)

id   start         end
1    2019-01-01    2019-02-01
2    2019-01-10    2019-01-15
3    2019-01-05    2019-01-10

The overall date ranges are 2019-01-01 to 2019-02-01. I would like to calculate the average difference between the start and end dates for each of the dates in that range.

The result would look exactly like this. I've included the actual values for the averages that should show up:

date          avg
2019-01-01    0
2019-01-02    1
2019-01-03    2
2019-01-04    3
2019-01-05    4
2019-01-06    3
2019-01-07    4
2019-01-08    5
2019-01-09    6
2019-01-10    7
2019-01-11    5.5
    .         .
    .         .
    .         .