How do I represent an enormous bar plot with very long axis labels in R and ggplot?

Question

I have a ggplot of bar graphs for each cluster.

The axis labels ("Path") for the bar plot are all unique and long, but they are grouped by "PathTypes" and "Cluster" - info which I want to represent on the bar graphs. I use a texture (stripes, dots, etc) from the ggpattern package to represent the "PathType" and I use colors to represent the "Cluster".

The resulting graph I produce is illegible bc it's just too large. I've been butting heads with facet_grid and facet_wrap. I am fine with using 2-3 pages to represent all the clusters, but I'm unsure about how to split the data smartly to accomplish that.

Example code follows:

library(data.table)
library(ggpattern)
library(gridExtra)
library(ggpubr)
library(truncnorm)
library(ggplot2)
library(stringi)

# generating sample data for data table called all.cluster.dt 

PathType <- sample(x = c("Type1", "Type2", "Type3", "Type4", "Type5"),   # create the PathType column
                   size = 400,
                   replace = T)
Score <- rtruncnorm(n = 400, a = 15, b = 90, mean = 55, sd = 15)     # create the Score Column

Path <- NA     # initialize the Path column
Path.generator <- function() {     # function to write unique Paths
  a <- do.call(paste0, replicate(10, sample(LETTERS, 15, TRUE), FALSE))
  single.Name <- paste(a, collapse = ' ')
  return(single.Name)
}

cluster <- sample(x = c(1:14),    # create the Cluster column
                  size = 400,
                  replace = T)

all.cluster.dt <- data.table(     # create the data table with desired columns 
  PathType,
  Score,
  Path,
  cluster
)

for(i in 1:length(all.cluster.dt$Path)){     # loop down Path column calling function to generate unique Path name for each row
  all.cluster.dt$Path[i] <- Path.generator()
}

wrap.it <- function(x, len)     # function to try and wrap long Path label text 
{ 
  sapply(x, function(y) paste(strwrap(y, len), 
                              collapse = "\n"), 
         USE.NAMES = FALSE)
}

# Call this function with a list or  vector
wrap.labels <- function(x, len)
{
  if (is.list(x))
  {
    lapply(x, wrap.it, len)
  } else {
    wrap.it(x, len)
  }
}

wr.lap <- wrap.labels(all.cluster.dt$Path, 40)     # wrap Path labels to 40 characters long
all.cluster.dt$Path <- wr.lap

all.cluster.dt$Path <- factor(all.cluster.dt$Path,     # group and factorize the data by PathType and Score
                          levels = unique(all.cluster.dt$Path[order(all.cluster.dt$PathType, all.cluster.dt$Score)]))

cluster.color.df <- data.frame("cluster" = c(1:14),     # add custom colors to represent which Cluster the Path belongs to
                               "color" = c("#F5F2D4", "#CAD8F2", "#8FB6FF", "#FFFDD7", "#DADADA", "#DAEB9B", "#EED1F2", "#C9E2D0", "#FFDFA2", "#DFFFD6", "#F6DFDE", "#E2DEF5", "#F0B8BC", "#CAF3EF"))
setDT(all.cluster.dt)[cluster.color.df, color := i.color, on = .(cluster)]     # match color to cluster in all.cluster.dt

bar.plots <- ggplot(all.cluster.dt, aes(x=Score, y=Path)) +
  ggpattern::geom_col_pattern(     # adds texture/patterns to the bars based on the PathType column
    aes(pattern = `PathType`),
    fill = all.cluster.dt$color,
    colour = "black",
    pattern_density = 0.2,     # how dense the pattern should be
    pattern_fill = "black",
    pattern_spacing = 0.1) +
  scale_x_continuous(expand = c(0, 0), limits = c(0, 90)) +
  theme_bw() +
  theme(axis.title.y = element_blank()) +
  theme(legend.position = "none",
        text = element_text(size = 8)) 

bar.plots + facet_grid(rows = vars(cluster), scales = "fixed")     # draw the bar graph

I now attempt to use grid.arrange and ggsave to arrange the plots by Cluster on a page, but get an error: "replacement has 17 rows, data has 400"...

pdf("bar_graphs.pdf", wi=8.1,hei=10.6)

do.call(grid.arrange, bar.plots)
ggsave("bar_graphs.pdf", marrangeGrob(bar.plots, nrow=4, ncol=2))

dev.off()

Any answers that provide the overall solution to my goal (getting my bar graphs into a legible figure) or elucidate why I get an error arranging grobs is much appreciated.