In Sublime you can navigate files an functions with ctrl/cmd + P or directly functions in the same file with ctrl/cmd + E.
If you don't press enter after watching, you can press escape, and go back to where you were and keep on writing.
I'm sure what you are looking for is perfectly possible with a python script... it's even probable that someone has already done a package for that. Install the Package Manager (google it) and then look for other PHP packages that extend the default PHP behaviour. There are tons of community packages with custom functionalities.
I've never used PhpStorm, but is it like the functionality built into the CTags plugin. Specifically the "Show Symbols Multi" functionality? I've never used it with PHP, but I have in some of the Python code I have written. I think that is what you are looking for. There may be other plugins with similar functionality, this one just came to mind.