Matching pair-wise columns from left to right across rows in one dataframe to another dataframe and adding new columns with matching values

I've got a dataset like this:

 df1 <- data.frame(    col1 = c(1, 2, 3),    col2 = c(4, 5, 6),    col3 = c(2, 8, 9),    col4 = c(5, 11, 12),    col5 = c(13, 14, 15),    col6 = c(16, 17, 18),    col7 = c(19, 20, 21),    col8 = c(22, 23, 24)  )

and a second that has a 'key' of matches that I'm looking for in df1 :

df2 <- data.frame(    colA = c(1, 2, 3),    colB = c(4, 5, 6),    value = c(100, 200, 300)  )

what I'm trying to do is find each pair-wise column match from left to right and create a new column containing the value from df2 everytime there is a match so that it looks like this:

 df3 <- data.frame(    col1 = c(1, 2, 3),    col2 = c(4, 5, 6),    col3 = c(2, 8, 9),    col4 = c(5, 11, 12),    col5 = c(13, 14, 15),    col6 = c(16, 17, 18),    col7 = c(19, 20, 21),    col8 = c(22, 23, 24),    match1 = c(100, 200, 300),    match2 = c(200, NA, NA)  )

I've tried this kind of approach:

df_match <- inner_join(df1, df2, by = c("col1" = "colA", "col2" = "colB"))  df1$matched_value <- df_match$value[match(paste(df1$col1, df1$col2), paste(df_match$col1, df_match$col2))]

but it only returns one match across the rows. The other issue is I'm running this through many iterations that have varying numbers of columns in df1. I'm thinking I need something along the lines of across rows starts with 'col' but I'm pretty stuck.