The problem you have is that a deployment has to be a perfect contractual match: nothing can change apart from your title and department. You must keep the same pay grade, the same employee status (Term/Indeterminate), and you'd also be stuck with the same contract expiry date. (Although once you start with the receiving department, they're free to extend your contract through the usual channels.)

So if you're currently, say, a term CR-03 with an expiry date of July 31 2018, then you need to find a manager who wants a term CR-03 with an expiry date of July 31 2018. If they want literally anything else, they can't take you.

If you have rare skills, or you're at least B/B/B bilingual and have skills which don't often map onto bilingualism (computers, paralegal, science or science administration, etc.), you actually have an okay shot, although this gets much dicier if you can't get a reference from your current department.

If you don't have either of those going for you, then cold-calling managers and begging for a deployment is going to be a game of chance, and one you're likely to lose: you're looking for that perfect contractual match, and even if a given manager has an opportunity which you would be legally permitted to deploy into, most managers looking for entry-level hires already have pools they can draw upon and are working through that process rather than sitting around waiting for deployment-eligible people to call them.

You can get on GConnex and join the job seekers' board, but it's really only useful in the NCR, and it's a public platform -- so word might eventually get back to your manager. It's probably a better shot than cold-calling, at any rate.

And there are other options. For example, some departmental staffing advisors (or generic HR people in tiny departments and agencies) keep internal lists of employees who are looking for deployments: I know several people who've bounced out of an awful job through such a list, although you need to be aware that this can backfire. (If your HR people keep it confidential and are sensitive to your need to escape a toxic environment, your manager won't know you're trying to get out until you're already halfway out the door; if HR lets it slip and your people take it the wrong way, then your workplace's level of toxicity might jump a few notches.)

Frankly, though, I think your best option is to take full advantage of Personnel Selection Leave and start applying for other jobs.