In my career I had lots of good ops people transition into a variety of other IT roles, even help desk support. Have you considered finding an ops position in a company that has such succession plans in place? This might be a transition you need to make “within” a company. Leverage the skills you have now to get a position fitting with your skill set in an organization that will provide career paths.
I think the market is just too tight right now to expect an external transition, and certainly not if you are out of work now…recipe for disaster IMO as no amount of self study will be valued like on-the-job experience.
However, there is a different path you could follow. There are opportunities out there for non-technical customer support service jobs you could land. That is another viable career path into technical help desk. Get the experience doing customer support, grow to a technical role in that company if possible, but even if you need to move on you have the tougher half the skills under your belt that are valued by employers looking for technical help desk support. Many help desk employers feel they can teach the technical stuff easier than teaching someone to deal calmly and effectively with customers.