How would you get a time out in a background job? Are you sure it's not some other short dump?
These FMs are not released, so why are you using them? It looks like they only do some "reading" here, so why not replace them with custom SELECTs that you can tailor to your requirements?
As others noted, there are many tools available in SAP (e.g. this one) to analyze and resolve performance issues. I feel using parallel processing here would be nothing but a band-aid on an ugly sore.