Meaning the hashrate did not throttle when the card was plugged into a monitor?  If so that would be pretty conclusive that rdluffy was on the right track.  Using the dummy plugs in your cards that he suggest (or leaving the cards plugged into monitors) would solve the problem but in my opinion it would be better to find the low-power setting that is causing the cards to throttle, and turn it off.  If by "The cards work fine when plugged into a monitor." you mean they produce a proper display but the hashrate continues to throttle you can rule out low-power "sleep" modes as your culprit.

When diagnosing problems like this it's a good idea to remember the cardinal rule of computers:  Computers do exactly what you tell them to, not what you want them to.  Somehow you've told your miner that it should be throttling down the cards.  Maybe you did it explicitly through a setting you chose; more likely you did it implicitly through the software you've installed.  Try flashing back to stock bios, using Win10, etc...Once you find a configuration that works see if you can reproduce your problem.  That will tell you how to fix the problem in your desired configuration.