I think three things are critical in evaluating management, i.e. innovation (as you brought up), leverage/debt and long-termism.

Many people don't realize that innovation and leverage are negatively correlated. As Nassim Nicholas Taleb rightly pointed out that getting into debt increases fragility, hence leading to MUCH lower tolerance of failure.

Innovation, on the other hand, requires a lot of failures (ask Elon Musk, Larry Page and Thomas Edison). It is not a coincidence that highly geared companies are often lacked of innovation, because they have a bank to feed. Too geared to fail!

Innovation is like breathing, you don't wake up one day and say "I want to breath the 'innovation' air". It's a culture that the management must induce since day 1 and hoping someone, on day 568, says "ah I have an idea!", instead of instructing everybody TO BECOME innovative on day 567.

And no, with all due respect, innovation itself has no process. It is a culture and attitude, and it starts with the top guy. To have a process for innovation is counter-intuitive. Freedom is what innovators need (ask Larry Page).

Finally, LONG-TERMISM. Still on innovation: one needs to think long term, or some call it 'be visionary' to be innovative. Those who forever think about achieving better profit margin than their competitors in the next quarter will stay in the rat race forever. They are likely to achieve incremental results but not a breakthrough performance. Deploying capital into long-term projects is about willingness, not ability. (For this case, ask Larry Fink but not Carl Ichan)

I know it's hard to judge the innovative culture and long-termism of a management (especially when they are new), we can start with the one that hates debt first.