Changing a sole proprietorship into an LLC
Unfortunately, there is no good way to convert sole proprietorship, which is what you are now, into an LLC. More than that, you cannot even register your LLC under the same name as your current business until you cancel your DBA, because the state will not allow two businesses to exist under the same name.
Once you start the LLC, it will be a completely new legal entity and it will need a new EIN and a new State Tax ID. So, in a sense, you will be starting over.
To ensure a continuity of business, I would just form an LLC under a slightly different name then your current business, get everything set up and then start transferring your clients to the new company, before you shut it down. You should eventually shut down your current company to avoid any confusion.