Setting a pattern or symbol as NA value in geom_tile

I have data i want to visualise using geom_tile. The data deal with references in text data from either Germany or Spain to other European countries.

Example data:

data<- tribble(
  ~Ref_country, ~Country, ~Share,
  "ENG", "DE", 0.27,
  "ENG", "ES", 0.24,
  "ESP", "DE", 0.21,
  "ESP", "ES", NA,
  "GER", "DE", NA,
  "GER", "ES", 0.13,
  "FRA", "DE", 0.11,
  "FRA", "ES", 0.18,
  "ITA", "DE", 0.1,
  "ITA", "ES", 0.17,
  "POR", "DE", 0.03,
  "POR", "ES", 0.07,
  "RUS", "DE", 0.02,
  "RUS", "ES", 0.02,
  "NLD", "DE", 0.04,
  "NLD", "ES", 0.01,
  "BEL", "DE", 0.02,
  "BEL", "ES", 0.03,
  "SWE", "DE", 0.01,
  "SWE", "ES", 0.01
)

Since i do not count references from a country to itself, GER-DE and ESP-ES are NA.

I plot this with ggplot, geom_tile and scale_fill_distiller:

x %>% 
  ggplot(., aes(x = Ref_country, y = Country, fill = Share)) +
  geom_tile(color = "white", linewidth = 0.1) +
  scale_fill_distiller(
    type = "seq",
    direction = 1,
    palette = "Greys",
    na.value = "white"
  )

resulting in the following

My question is: is there a way to distinguish the NAs not by color, but by pattern? Maybe through a creative application of ggpattern. Or alternatively, is it possible to add text ("NA") or a shape on top of the respective NA tiles? Since I will likely publish it in black and white, color is not a good distinguishing property.

Thanks in advance.

PS: As another alternative, can the color scale be restricted to greys that are clearly distinguishible from white?

As you mentioned in your comment, the first option which came to my mind would be to use a "transparent" color for the missings. Additionally I switched to guide_bins for the legend. And of course could you also add a symbol for the missings using e.g. a geom_text layer or perhaps a geom_point:

library(ggplot2)
library(magrittr)

data %>%
  ggplot(., aes(x = Ref_country, y = Country, fill = Share)) +
  geom_tile(color = "white", linewidth = 0.1) +
  scale_fill_distiller(
    type = "seq",
    direction = 1,
    palette = "Greys",
    na.value = "transparent",
    guide = guide_bins(axis = FALSE, keywidth = unit(1, "cm"))
  ) +
  theme(legend.position = "bottom")

data %>%
  ggplot(., aes(x = Ref_country, y = Country, fill = Share)) +
  geom_tile(color = "white", linewidth = 0.1) +
  geom_text(data = ~ subset(.x, is.na(Share)), aes(label = "X")) +
  scale_fill_distiller(
    type = "seq",
    direction = 1,
    palette = "Greys",
    na.value = "transparent",
    guide = guide_bins(axis = FALSE, keywidth = unit(1, "cm"))
  ) +
  theme(legend.position = "bottom")