Would it be possible for your team to start a small VC firm instead of a startup? Wouldn't that be a better fit for a team that has lots of capital, one technical partner, and one sales partner, but currently doesn't have an idea?
I was going to say it might be worth looking for projects that have been validated by sales and then looking to grow them both with the team and capital.
Having something like a space with a couple ideas/ startups in it that have already been validated would lower your risk and expose you to more opportunities while growing the business. I assume.
That said, PE has plenty of opportunities within tech though. Which is essentially what you described.