Authorship of PI and/or other advisor on independent work?
There have been a number of discussions on this site about authorship, and looking at the authorship tag will reveal them. 

Ultimately, the conclusion of all those discussions has been that conventions on authorship are field-dependent and define "contribution" in different ways for different areas. In your case, it sounds like your advisors have both encouraged you to work together and have not requested authorship. Since the usual response to questions like yours would be 'ask your advisor', it sounds like they've answered, by saying that you don't need to include them. But I'd check with them anyway.

The remaining part of your question deals with purely tactical considerations: to whit, 


  Can augmenting the author list increase chances of the paper being accepted for publication ? 


I think the consensus on this site, and in general, is that misrepresenting or exaggerating contributions for any reason would be considered quite unethical (where again contributions must be evaluated in a field-specific manner). 

The work must stand or fall on its own merit, and be reviewed accordingly. It might be rare in your community for graduate students to author papers without PIs, but there's always a first time (and in my community it's quite common). 

On the more mundane issue of paying for publication (I assume you're thinking of one of the open access journals that charge such an amount), that's a discussion for you to have with your advisor(s) before submission. They might suggest alternate journals, or even be willing to pay the fees (again, the equivalent would be a PI in my field paying for a student to attend a conference and present a paper not co-authored by the PI: this is also quite common)