Removing specks from shape in R

Question

After dissolving inner boundaries, this sf shape [Pastebin] retains residual specks or crumbs:

library(sf)

#download file "shp.txt" from Pastebin
shp <- dget("shp.txt")

class(shp)
[1] "sfc_MULTIPOLYGON" "sfc"

plot(shp)

I have tried 2 different methods of removing them but both fall short:

#CRS is in meters so that threshold parameters are expressed in square meters in both methods
st_crs(shp)$units 
[1] "m"

#Method #1
library(rmapshaper)
shp <- ms_filter_islands(shp, min_area=1000000)
plot(shp)

Method #1 fails to remove at least one tiny speck in the centre of the shape:

#Method #2
library(smoothr)
shp <- drop_crumbs(shp, threshold=1000000)
plot(shp)

Method #2 doesn't do anything, apparently.

What are substitute or complementary ways of accomplishing the task?