In my own company, we were able to grow from $20M in sales to $32M in 3.5 years without adding even one extra person! People went from working 45-60 hours per week to having more time to spend with their families. This was all done by convincing everyone to spend 20 minutes every day eliminating the things that got in their way. I called this Rapid Kaizen, and A3 was the way it was executed via temporary self-directed work teams. Contrary to popular belief, the more committed we were to Rapid Kaizen, the more time we seemed to have to do.....well more Rapid Kaizen. Literally thousands of hours of frustration in the form of the 8 wastes were eliminated by the people who actually do the work.
Go ahead and bite the bullet. Start today, what do you have to lose? Just go ask people what frustrates them about their job, what slows them down, and what they'd change right now if they could. Spend 20 minutes daily yourself helping them and then watch a spark turn into a blaze. People want to do what they think is important to their leaders. Show them that frustration elimination is important to you.
Suddenly, one day, you will wake up, go to work, be chaos-free, and have time to spare to delight (not satisfy) your customers.