Mmmm, not as complete an answer as I was hoping to be able to provide, but I do have some thoughts to share. Maybe they will trigger some further thoughts from me or other folks...
Firstly, your images are lacking TIFF tag 262 ("Photometric Interpretation") which is upsetting several tools you might otherwise use. What program generated the images - as they are not strictly compliant? Can you correct/improve the program that generated the images?
I managed to set the "Photometric Interpretation" tag to "min-is-black" with:
tiffset -s 262 0 YourImage.tif
Once that is set, I managed to use vips
(from here) - which is exceedingly fast, and memory-efficient, to convert your file to JPEG. It has Ruby and Python bindings if you prefer those languages.
So, the command-line in Terminal to convert your file to JPEG is:
vips im_vips2jpeg YourFile.tif result.jpg

I am not convinced that works correctly though, so maybe John @user894763 (the author of vips
) would take a look.
Another thought, using vips
is that the following command will save a raw RGB file of 3 floats per pixel which you can read straight into your own program without any decoding at all:
vips rawsave YourFile.tif image.raw
-rw-r--r-- 1 mark staff 3145728 20 Jun 16:59 image.raw
You'll note that the file size (3145728) corresponds to:
512 pixels * 512 pixels * 3 RGB values * 4 bytes of float each
I also used ImageMagick to convert your image to JPEG, with
convert YourImage.tif result.jpg
and got this result:

A further thought that occurred to me was that you could pre-warm your buffer cache before running your own TIFF extract program, by running cat
on each of your files to cause them to be fetched from the NFS server:
cat *.tif > /dev/null
or maybe run parallel streams of that to reduce latency.
Another thought was that you could pre-fetch the files to a RAM-backed filesystem so that your files can be read with minimal latency. At 186kB per file, you could get 5,000 in a 1GB RAMdisk for much faster processing:
mkdir /tmp/RAM
sudo mount -t temps -o size=1G temps /tmp/RAM
You could also put intermediate files that I suggest in my thoughts above into the RAM filesystem.