MySQL Hardware Bottleneck
MyISAM or InnoDB?  Depending on which, you need to see the appropriate cache buffer.  If you had 16GB of RAM, you could set that so that the table will (eventually) be entirely in RAM.  That would move it from being I/O bound (as it probably is now) to being CPU bound.  At that point, an old, slow, cheap, spinning drive will be almost as good as SSDs.

Can you parallelize the algorithm?  If so, split it into as many programs (connections) as you have cores.  That will (assuming CPU-bound) give you a nice speed-up.

Let's see the main query.  And the SHOW CREATE TABLE for any table(s) involved.  There may be simple ways to speed it up.

(I estimate that a table of 8.4GB is about the 96th percentile.)