Yes, for outdoors shooting it's hard to beat the "magic hours" of sunrise and sunset - and the two to three hours after sunrise and before sunset aren't too bad either. But what do you do with that "11-3" slot? Here's two scenarios to try.
Get in Close
The harsh mid-day light will have less impact on your shots if you get in close to the subject and eliminate any background elements. You purposefully minimize the high contrast range in your shot. The engine shot above was at high noon. By getting in close I eliminated the bright sky and white concrete - not to mention the reflections off the leading wing edges.
You don't like HDR you say? Really? Maybe it's the "grungy" HDR that doesn't suit your style?
Remember, that "grungy" and exaggerated look is only one style of HDR. High Dynamic Range photography can look anywhere from very natural all the way to over the top. Shooting HDR at high noon (the way the second image above was shot) makes the lighting conditions virtually irrelevant. Take 3 to 5 shots over a range of exposures, use your favorite HDR or stacking program and make a great natural looking shot.
Many More Ways
There are many other scenarios to use during "bad" lighting times, not just these. Plenty of interesting things can be found in the shade and a small diffuser can give you a bit of your own shade for smaller objects. Flowers, insects, old fences, abandoned equipment. Take the time to look and you'll find your mid-day shots!
Stay in Focus,