Solution based on @caldwellst code but with automatic ratio calculation:
insert_ratio <- function(tbl, where) {
    if(is.character(where)) {
        # if where is character we search it in the rowlabels
        where = grep(where, tbl[[1]], fixed = TRUE)[1]
    }
    isTRUE(where>1) || stop("'where' should be greater than 1 for ratio calculation.")
    isTRUE(where<=NROW(tbl)) || stop("'where' should be less or equal than number of rows in the table.")
    tbl1 <- tbl[1:where,]
    to_insert = c(row_labels = tbl[[1]][where], tbl[where, -1]/tbl[where - 1, -1]*100)
    tbl2 <- tbl[(where+1):nrow(tbl),]
    tbl1 %>%
        add_rows(to_insert) %>%
        add_rows(tbl2)
}
insert_ratio(test1, 2)
 # |     |              |    vs |      |
 # |     |              |     0 |    1 |
 # | --- | ------------ | ----- | ---- |
 # | cyl |            4 |   5.6 | 71.4 |
 # |     |            6 |  16.7 | 28.6 |
 # |     |              | 300.0 | 40.0 |
 # |     |            8 |  77.8 |      |
 # |     | #Total cases |  18.0 | 14.0 |
insert_ratio(test1, "cyl|6")
 # the same result
UPDATE
Ratio calculation is moved to separate function:
ratio = function(tbl, where, label = NULL){
    if(is.character(where)) {
        # if where is character we search it in the rowlabels
        where = grep(where, tbl[[1]], fixed = TRUE)[1]
    }
    isTRUE(where>1) || stop("'where' should be greater than 1 for ratio calculation.")
    isTRUE(where<=NROW(tbl)) || stop("'where' should be less or equal than number of rows in the table.")
    
    if(is.null(label)) label = tbl[[1]][where]
    c(row_labels = label, tbl[where, -1]/tbl[where - 1, -1]*100)
}
insert_row = function(tbl, where, row) {
    if(is.character(where)) {
        # if where is character we search it in the rowlabels
        where = grep(where, tbl[[1]], fixed = TRUE)[1]
    }
    isTRUE(where<=NROW(tbl)) || stop("'where' should be less or equal than number of rows in the table.")
    first_part = seq_len(where)
    tbl1 <- tbl[first_part,]
    
    tbl2 <- tbl[-first_part,]
    tbl1 %>%
        add_rows(row) %>%
        add_rows(tbl2)
}
insert_row(test1, 2, ratio(test1, 2))
insert_row(test1, "cyl|6", ratio(test1, "cyl|6"))