There are only two ways to speed up loading data - buy a faster hard drive, or read less data from it :P
I can't help with the former, but for the latter you could try converting your FASTA files to 2bit and load that. A 6Gb FASTA file will only be 1.5Gb in 2bit format - and that's before compression. It might even fit into RAM as 2bit, and a quick Google suggests that there are packages in R which understand the 2bit format. I don't know if it then converts it to something else after reading it... who knows.
But 6Gb isn't much data really... hard drives typically read over 100MB/s, so unless 60 seconds is too long for you, I doubt getting more bang for your RPM is going to make a difference. Most likely the logic part of your program is the slow part, not the reading part. R is a famously slow language, particularly in its loops, which is why packages like plyr exist to try and speed things up.
But all of this is just speculation - since we don't know what your program does, we cannot really say how to speed it up. If you really want to speed up your code (and become a better programmer in the process) definitely check out this: http://adv-r.had.co.nz/Profiling.html
Good luck! :)
Why do you need R? Can't you use another program for your project? linux pipeline, C, etc...
No particular reason, I'm slightly more familiar with R and I'm not sure how to translate my script into another language