How can I move x-axis labels away from the centre of a ggplot that uses coord_polar?

I'm making a polar-transformed barplot in which several of the x-axis labels overlap with the plot area. For context, I'm working on a shiny application that you can find a copy of here (not any more).

I've tried using theme(axis.text.x = element_text(vjust = -someNumber)), but it doesn't seem to be doing anything.

Here is a reproducible example to demonstrate the problem:

## Tiny example plot
### Libraries
require(dplyr)
#> Loading required package: dplyr
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
require(ggplot2)
#> Loading required package: ggplot2

### Data
categories <- c("foo", "bar", "baz", "biff", "zoop", "sesquipedalian")
values <- c(100, 150, 42, 135.45, 177, 182)

plotThis <- tibble(names = categories, values = values)

### Plot the plot

ggplot(plotThis, aes(x = names, y = values)) + 
  geom_bar(stat = "identity", color = "black", fill = "blue", width = 1) + 
  coord_polar(clip = "off") +
  theme_minimal() +
  scale_y_continuous(name = NULL, breaks = NULL) +
  xlab(NULL)

^{Created on 2022-02-15 by the reprex package (v2.0.1)}

How can I move the 'sesquipedalian' label (or, if necessary, all labels) further away from the centre so that it does not overlap with the plot?

This doesn't look nearly as nice as the answer from @Allan Cameron using his very slick {geomtextpath} library but has the (possible) advantage of being easy to implement with native {ggplot2}. Here we simply use expand_limits() in the y direction to push the axis further from the plot and leave room for the label. It's a bit of a hack because I came up with a fudge factor for how far to expand based on the length of the label and the size of that bar. It works OK with labels of a certain size but if they get really long it will break down a bit unless you introduce a line break. Also you can add theme(plot.margin = unit(c(3, 0, 3, 0), "lines")) to get more space around the plot to avoid cutting of super long labels.

library(tidyverse)

# data
plotThis <- 
  tibble(
  names = c("foo", "bar", "baz", "biff", "zoop", "sesquipedalian"),
  values = c(100, 150, 42, 135.45, 177, 182))

# calculate scaling of axis based on longest label
new_max_y <- 
  plotThis %>% 
  mutate(nchar = nchar(names),
         new_max_y = values * (1 + 0.01 * nchar)) %>% 
  pull(new_max_y) %>% 
  max()

# plot - expand margins if names get really long
plotThis %>% 
  ggplot(aes(x = names, y = values)) +
  geom_col(color = "black", fill = "blue", width = 1) +
  coord_polar(clip = "off") +
  theme_minimal() +
  scale_y_continuous(name = NULL, breaks = NULL) +
  expand_limits(y = c(0, new_max_y)) +
  xlab(NULL)

^{Created on 2022-02-15 by the reprex package (v2.0.1)}