Hi Andrew and welcome to the forum.
Low bandwidth and medium or high resolution grib files just don't go together.
With a satphone the best com rate is 2400 bits/sec which is very slow. This dictates file sizes of about 20 kbytes as the largest reasonable and it would take some 5 minutes to download. To meet the target file size one needs low resolution grib files 1 or 2 degrees and also with larger time steps - 12 or 24 hours instead of 3. One would also need to reduce the number of variables - perhaps wind only or wind and pressure at sea level.
It is possible to use Xygrib to select a minimal GFS grib (lowest res is 1deg) and download it using a satphone data connection, however, this is not the most efficient way to do the job.
POP3 email protocol (pulling an email from a mail server) is more efficient and tolerant to both low bandwidth and low latency (response times). There are mail servers that are optimised for satphone data connections and use compression to get more data down over the slow connections. Most of these mail server charge a fee but it is worth the money.
Now to getting the data (small grib files). I suggest that you use a free data retrieval system based on emails called saildocs.com. If you a planning an ocean crossing you really need to investigate this resource combined with a suitable mail server and a suitable mail client on the computer connected to the satphone.
With saildocs it is very easy to get small gribs and other valuable weather resource to you via email.
I hope this answers some of your questions
David