Have you investigated a javascript compiler -- https://developers.google.com/closure/compiler/ ?
I've looked into a compiler, but my code is partially dynamically built using PHP, so it may not be a solution for me; I'm investigating that. Thanks for the link for the javascript profiler info below too; I'll see if that identifies anything that can be improved.
Your storage system could be the limiting factor. It is the slowest part of a computer (assuming your data is local to the computer). If not, then the network is the slowest part. CPU clock speed, CPU cache and RAM are usually the next contributing factors. What hardware are you running on now?
Once my research data is loaded into the script, it's not reading or writing to the disk; would the storage system have anything to do with just the script that's running, or is it only when I'm reading/writing to disk?
My script is run locally on my computer which is running XAMPP, so my computer is the server; when you say "network" you mean if I were running it off a different server, right? So I think for me that's not part of the issue.
For CPU cache, I see something like this in specs: L3 Cache Per CPU - 8 MB. Is it the size (8 MB) that's important, or the L3 part?
You may have written the script inefficiently. Have you run a javascript profiler -- https://developers.google.com/web/tools/chrome-devtools/rendering-tools/ ? A profiler will identify where in the code time is being used and how many times a line of code is being executed. For example if you are doing I/O a byte at a time rather than a 1K byte your code will be much less efficient.
Sometimes a hardware upgrade is the right answer, sometimes fixing inefficient code is the only answer.