Ordering geom_bar plots of frequency by multiple factors

Question

I'm creating a bar plot to display the number of survey responses from each county, and I want to group the responses by county and region. My data looks like this:

head(df)
# A tibble: 6 x 4
  responseid region     county      industry             
       <dbl> <fct>      <fct>       <chr>                
1        137 West Coast Los Angeles Construction         
2        138 West Coast San Diego   Energy               
3        139 West Coast Orange      Professional Services
4        140 East Coast Queens      Restaurants          
5        144 West Coast San Diego   Energy               
6        145 East Coast Miami-Dade  Public Sector    

I'm running this code:

ggplot(df, mapping = aes(x = fct_rev(fct_infreq(county)), y = stat(count))) +
  geom_bar(aes(fill = region)) + 
  coord_flip()+
  scale_y_continuous() +
  ggtitle("Responses by County") +
  ylab("Number of Responses")+
  xlab("County") + 
  labs(fill = "Region") +
  geom_text(stat='count', aes(label=..count..), vjust = .5, hjust = -1)

Which generates this plot:

The plot is ordered by response frequency by county. I'd like to make it ordered first by region, then by response count. I want this same chart, but with all the West Coast counties in order from most to least responses, then the East Coast counties in order from most to least responses.

Faceting it doesn't give the effect I want, since it pulls the West Coast responses to a separate grid and you can't compare all the counties by the same y-axis anymore; faceting without the axis flip makes the county names overlap and become illegible.

I also tried to add an interaction argument like this but that didn't change the plot at all:

ggplot(df, mapping = aes(x = fct_rev(fct_infreq(county)), y = stat(count), group = interaction(region, county))) +
  geom_bar(aes(fill = region)) + 
  coord_flip()+
  scale_y_continuous() +
  ggtitle("Responses by County") +
  ylab("Number of Responses")+
  xlab("County") + 
  labs(fill = "Region") +
  geom_text(stat='count', aes(label=..count..), vjust = .5, hjust = -1)

Edit: This is what it looks like with facet wrap. I'm not a fan because it's harder to visually compare the bars when they don't start from the same y-axis:

If you remove the coord_flip, all the bars start from the same place, but then you can't read the county names at all.

Answer 1

I added the following two lines to the original plot to get the outcome I wanted. Thanks everyone who helped out!

facet_grid(region ~ ., scales = "free_y", space = "free") +
  theme(strip.background = element_blank(), strip.text = element_blank())