Think of BK as the ultimate trump card. Even if your BK is not filed before the upcoming hearing, little, if anything is likely to happen. By not appearing, you run the risk of having an Order for Contempt of Court, but if you file BK thereafter, the enforcement mechanism of any such order will be stopped by the BK. You can call the courtroom and opposing counsel to give them a heads up and case number (if you have one by then). If you are still nervous, show up at the court hearing and tell the judge that you are in process of filing BK and they will be subject to the provisions of the "automatic stay". Good luck.
I'm not sure how you're going to file your BK before Monday morning without filing it electronically, and only attorneys can do that using the ECF system. However, that aside, the moment your case is filed, electronically or otherwise, the automatic stay is in effect. The document you then file with the state court is a "Suggestion of Bankruptcy." This gives notice to the state court of the BK and the automatic stay, thus stopping the state court action. Good luck!
I often take cases other attorneys won't, so call me for a free consultation. My number is 727-712-3333, or you can view my website at www.TampaConsumerLawyer.com