Ok, having learnt a lot of stuff in the months since I asked this question, here are a couple of options:

In R, very similar to Bastien's answer:

library(raster)

rootdir <- 'C:/Users/obrl_soil/Downloads'
setwd(rootdir)
tinyraster <- raster('tinyrast.tif')
tinypolygon <- readOGR('tinypolygon.shp')

# alter your mask polygon to line up with the nearest pixel edges
tpoly_aligned <- alignExtent(tinypolygon, tinyraster, snap='near')

# clip and export in one hit
tinyclip <- crop(tinyraster, tpoly_aligned, filename='tinyclip.tif')

I noticed when checking the outputs in QGIS that writeRaster introduced some spurious data in the output tif, but crop didn't - e.g. input elevation for a pixel was 108.10545, output with crop was the same, but output with writeRaster was 108.10545349121094.

Alternate workflow - get the polygon bounding box coordinates and feed them into gdal_translate using -projwin. Just be careful which version of gdal_translate you use!. 1.11 is fine, and 2.1.2 should be when its released.

You can also do this in R, like

gtrans111 <- 'C:/Program Files/GDAL/gdal_translate.exe'
tinypolygon <- readOGR('tinypolygon.shp')
tpbb <- toString(c(tinypolygon@bbox[1], tinypolygon@bbox[4],
                   tinypolygon@bbox[3], tinypolygon@bbox[2]))
tpbb <- gsub(', ', ' ', tpbb)

system2(gtrans111, args= c('-projwin', tpbb, 'tinyraster.tif', 'tinyclip2.tif' ))

or even bypass creating any R objects by just inputting the polygon bounding coordinates directly

system2(gtrans111, args= c('-projwin', '148.665 -20.88 148.67 -20.884', 
                           'tinyraster.tif', 'tinyclip3.tif'))

The output extent is not identical to the raster package methods, but does align correctly. All of these methods are easy to loop across multiple datasets, which is the real advantage of R. You can do something similar in Python too.

Ok, having learnt a lot of stuff in the months since I asked this question, here are a couple of options:

In R, very similar to Bastien's answer:

library(raster)

rootdir <- 'C:/Users/obrl_soil/Downloads'
setwd(rootdir)
tinyraster <- raster('tinyrast.tif')
tinypolygon <- readOGR('tinypolygon.shp')

# alter your mask polygon to line up with the nearest pixel edges
tpoly_aligned <- alignExtent(tinypolygon, tinyraster, snap='near')

# clip and export in one hit
tinyclip <- crop(tinyraster, tpoly_aligned, filename='tinyclip.tif')

I noticed when checking the outputs in QGIS that writeRaster introduced some spurious data in the output tif, but crop didn't - e.g. input elevation for a pixel was 108.10545, output with crop was the same, but output with writeRaster was 108.10545349121094.

Alternate workflow - get the polygon bounding box coordinates and feed them into gdal_translate using -projwin. Just be careful which version of gdal_translate you use!. 1.11 is fine, and 2.1.2 should be when its released.

You can also do this in R, like

gtrans111 <- 'C:/Program Files/GDAL/gdal_translate.exe'
tinypolygon <- readOGR('tinypolygon.shp')
tpbb <- toString(c(tinypolygon@bbox[1], tinypolygon@bbox[4],
                   tinypolygon@bbox[3], tinypolygon@bbox[2]))
tpbb <- gsub(', ', ' ', tpbb)

system2(gtrans111, args= c('-projwin', tpbb, 'tinyraster.tif', 'tinyclip2.tif' ))

or even bypass creating any R objects by just inputting the polygon bounding coordinates directly

system2(gtrans111, args= c('-projwin', '148.665 -20.88 148.67 -20.884', 
                           'tinyraster.tif', 'tinyclip3.tif'))

The output extent is not identical to the raster package methods, but does align correctly. All of these methods are easy to loop across multiple datasets, which is the real advantage of R. You can do something similar in Python too.