Yep, most browsers prohibit the use of the file system api for this very reason... hence existing workarounds, sometimes limited, to a sandbox or similar...
I tested a couple of javascript workarounds for Firefox but our silk browser does not seem to like those.
It looks like implementing POST might be the only solution for variables over 2048 bytes here.
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Without details of what you're trying to do it's hard to give ideas, but another option to consider is to use a CGI or a web service that receive the value from the browser (e.g. a server on the PC or a public server with php or ASP.NET) and generate the file that you need to download.
Then use your new /download.ps3 command to get the file.