If your job is going to be a portfolio manager anyway, you're often better off being an actual portfolio manager. You make more money, pay lower taxes, and have more working flexibility. If you make most of your money from a W-2, even if you're the CEO, you've taken a bad deal. The real money is in ownership.
But that said, if you really want to be a director, here's some strategies I've observed for getting there.
1.) Scope and headcount. It's really all about headcount - that is the qualification for being a Director. Increased scope is how you get the headcount.
2.) Find out what upper management wants. Volunteer for it. That is how you get the scope.
3.) Attach strings to every request that your team takes on. "Well, we could be doing [important executive ask], but we don't have resources for it right now. If you gave us headcount for it, though, we'll make sure that it becomes our top priority." Attach a quid pro quo to everything. That is how you get the headcount.
4.) The same goes for requests from peer teams, but there needs to be some finesse here so you aren't labeled as difficult to work with. Oftentimes, it's best to dribble out easy requests as a teaser of good faith, but then say that for any larger projects, you need a line item in their budget that donates headcount to your team.
5.) Ruthlessly inflate the difficulty of everything you do. "Oh, why did it take 2 months to move a button around on the screen? We needed to get alignment from product and UX, then we needed to check with 2 other teams, then we needed to make sure that it works on all the platforms we support, we needed to make sure it didn't adversely impact the click-streams to advertisements on the page, ..." (Note that in some companies, it really does take 2 months to move a button around on the screen. If you work in one of those companies, message it as taking 6 months.). This is also your way to provide work/life balance to the people underneath you. If they want to work 4 hour days, this is good for you, because it means you need twice as much headcount to accomplish the same task.
6.) Deliver on your commitments, but only to the extent that it looks good in a demo or PowerPoint. VPs aren't up-to-speed on the details; that's why they are VPs, and have hundreds of people under them to worry about the details.
7.) If you do get called out on the details, offer some excuse and then request headcount to fix it.
8.) If your department is about to implode, immediately start talking to executive recruiters so you can get a director title elsewhere.
9.) Actually just start talking to executive recruiters anyway. It usually takes something like 18-24 months to get a director role externally, so if one happens to land in your lap, take it.