Your question seems to be, “Can I game the system and get away with doing what I want without facing the consequences?” The answer to that question, as it is under any circumstances, “Maybe.”
Amber points out the real problem. You can avoid getting fired from your current position but you can not get another without falsifying your request to have your clearance reopened. It doesn’t matter if the new agency doesn’t use JPAS. They are still going to ask you about drug use and you will have to lie. If you are OK with that, and willing to risk the repercussions, go ahead and give it a try.
Now, you don’t say what drugs you are going to test positive for. Your best chance MAY be to fess up, get yourself into a program (even if you don’t believe that you need it), get yourself into counseling (even if you think that you don’t need it), get yourself clean and show that you are contrite and concerned about the issue and it’s implications. If it grass and you can show that it was legal when you did it or if it was prescription or other drugs used to self-medicate for a physical problem, you may have a chance to work through this one.
My expectation is that there was nothing random about the drug test. They expect you to fail. They already know something about what you did. Who was with you? Has it been persistent or a one-time issue? Has your work or attendance suffered so that a coworker or superior may have reported you?
Get out in front as quickly as you can.
Or, if you are prepared to not work in cleared positions anymore, resign.