As you and your LBS probably know, there are generally two clearance dimensions, a somewhat conservative one from the manufacturer and then closer to the actual clearance dimension, the difference being extra room mostly for mud and dirt. On my road bike I tried 32-s which worked fine while the mfr. indicated 30. If I'd had disc brakes I could have gone wider.
However, I developed a preference for my MB in those situations and got rid of the extra tires/wheels but if I were on more compacted road surfaces and weren't looking for geometry relief from my road bike it might have worked.
I agree and have a further suggestion for
@Ron : You can almost always get more tire than the manufacturer says. Usually 3-5 mm minimum. So, how to find out w/o blowing a ton of money?
Go to a LBS you are sure will let you return unused merchandise. Buy a folding bead tire in a box. IOW, you want something you can return unused to its original package. If it is a wire bead with an adhesive tag around it, you can't do this. Even if you can't find a tire you WANT to put on the bike, you can do this and just consider it a fitting session. Grab a 32 and a 35 and try putting them on your rear wheel. You'll need to install it w/ a tube obviously, regardless of your ultimate plan (and tubeless IS the way to go, although much harder w/ these small tires than MTB).
My point for this is that a 28mm is still a pretty low volume tire, even if your rim squeezes it to 31mm, because it just changes the shape, not the volume. In my above plan, ymmv due to variation in sizing. But I think you will find a 28mm to be entirely inadequate. I have 28s on my road bike and I can tell you that the few times its been off pavement, well, I try to avoid this.
Also, you need to consider the wheel width. A wide array of tires and wheels will FIT together. The Great Sheldon Brown tells us the best fits:
http://www.sheldonbrown.com/tire-sizing.html
Look for a red/green grid near bottom of page. I've found that one, or even two sizes outside of his ideal will work w/o issues if your not doing 1% maneuvers. So, in the above trial sizing, you might find for example that 32 just barely fits and a 35 not quite. If you have say 13mm rims, you'll find that 17s or even 19s might allow that 35 to fit. You can get a decent set of wheels for $200-300, a lot cheaper than a whole bike.
I am building a "gravel grinder" with a steel frame and 35mm tires. But I haven't ridden it yet, so I can't tell you if 35mm will be adequate for non-technical dirt and gravel. But my hunch is it will be.