How do I move ggplot strip labels so that there is one on top and one on the right and only label colums and rows instead of every plot

The ggh4x::facet_grid2() function allows for independent scales within columns or rows in a grid layout. Disclaimer: I'm the author of ggh4x.

library(tidyverse)

dat <- tibble(River = c(rep(letters[1:6],27))) %>% 
  mutate(cohort=rep(seq(2007,2015,1),18),
         mu = c(rnorm(54,300,25),
                rnorm(54,0.5,0.15),
                rnorm(54,-0.75,0.1)),
         param = c(rep('var1',54), 
                   rep('var2',54),
                   rep('var3',54))) %>% 
  group_by(param) %>% mutate(
    upr = mu+2*sd(mu),
    lwr = mu-2*sd(mu)) 

p1 <- ggplot(data = dat) +
  geom_point(aes(x=cohort, y=mu)) +
  geom_errorbar(aes(x=cohort, ymin=lwr, ymax=upr),
                width=0)

p1 +
  ggh4x::facet_grid2(factor(River) ~ param,
                     scales = 'free', independent = "y")

^{Created on 2022-01-13 by the reprex package (v2.0.1)}