Using st_distance with apply functions and iterators

I’m working with a dataset of islands in which I need to calculate the distance between each island and the nearest landmass with an area greater than that island. I can do this successfully with a for loop, but this takes too long and I want to rewrite the code so that it can eventually work with parallel processing and apply functions.

Here is example code for the for loop:

library(rgdal)
library(tidyverse)
library(sf)
library(spData)

alaska <- alaska

#this dissolves all features to remove internal divisions and 
#then converts multi-part polygons to single part. This
#effectively creates a separate feature for each isolated
#geometry (i.e. island)

alaska <- alaska %>% 
  st_buffer(0) %>%
  summarise(area = AREA) %>% 
  st_cast("POLYGON")

#recalculate area for each island
alaska$area <- alaska %>% 
  st_area() %>% 
  units::set_units(value = km^2) %>% 
  as.numeric()

#spatial object with Alaska landmass still included
alaska_all <- alaska 

#spatial object with Alaska landmass removed, leaving only islands
alaska_islands <- alaska[!alaska$area == sort(alaska$area, decreasing = T)[1],]


for (i in 1:nrow(alaska_islands)){
  d <- st_distance(alaska_islands[i,],
                   alaska_all[alaska_all$area > alaska_islands$area[i],],
                   by_element = T)
  alaska_islands$nn[i] <- sort(unique(d))[1]
}

What I’m having trouble figuring out is how to keep the alaska_islands$area[i],] iteration as part of the function. I’ve tried apply, lapply, and mapply and have had limited success. The most successful thus far has been:

apply(st_distance(alaska_islands, alaska_all[alaska_all$area > alaska_islands$area[i],]), 1, min)

but it seems to ignore the iterator. Some islands return the correct values (i.e. same as from the for loop) while others simply return 0.

sapply(1:nrow(alaska_islands), 
  function(i){
    min(
     st_distance(
       alaska_islands[i,],
       alaska_all[alaska_all$area > alaska_islands$area[i],])
     )
     }
  )

 [1]  59657.8767  25262.5830   5546.5902  51010.3289  18465.6949   4590.8588
 [7]   5137.2093   5379.8038   3629.5807   7366.8446    190.1415   5194.3717
[13]   4258.3425   7284.6550  18060.4840  43035.8838   7747.8683  28012.9886
[19]   8728.0644 176939.7554  33350.3792  51818.7938   2178.2563 343380.1486
[25] 253544.2871   2653.4898  18492.8536  14964.9450   8390.1484  15273.4045
[31] 250720.1601   7470.6006   8685.0207   3328.7401  11072.0120  16976.9256
[37]   7945.7566   6188.7005  38892.5618 158952.4960  12986.4244   3583.9433
[43]   4802.9676  54793.4105   3607.2833  90103.9748  14677.1710  21871.5170
[49] 564263.9674