Conditional mutating with regex in dplyr using rowSum

Let's say I have the following df

test = read.table(text = "total_score_1 total_score_2 partner_total_score_1 total_score_3 total_score_4 letter
                  1 -1 1 1 -1 B
                  1 1 1 -1 1 C
                  -1 -1 -1 -1 1 A", header = T)

I'd like to match all columns that contain "total_score" but NOT the word "partner" and then create a new measure that sums across all "total_score" columns, treating the -1 as 0.

I'm able to take a basic rowSum like so

mutate(net_correct = rowSums(select(., grep("total_score", names(.))))

Note, however, this does not exclude the possibility of matching the word "partner", which I wasn't able to find out how to do within a single grep command.

However, I'd now like to create a total_correct value which is a rowSum on the same columns except the -1s are treated as 0s.

This would result in a data.frame like so:

  total_score_1 total_score_2 partner_total_score_1 total_score_3 total_score_4 letter total_sum
1             1            -1                     1             1            -1      B         2
2             1             1                     1            -1             1      C         3
3            -1            -1                    -1            -1             1      A         1

One way might be to just count the total number of "1s" (rather than actually doing a sum), but I could not figure out how to do so within a mutate command