No two ways about it, tents are heat traps when they’re in the sun. That is one reason why it’s always prudent to pitch a tent in as much shade as possible聴no amount of mesh will keep a sun-baked tent that comfortable. Plus, sun is murder on tent fabrics, so if you can keep it in the shade, it will last much longer.
Now, as for your question about ditching the fly entirely and suspending a tarp above the tent: That makes perfect sense. The heat you feel in the tent when it’s in direct sunlight all comes from solar gain. Take that away and the interior temperature will be the same as the ambient air temperature. Plus you accrue the benefits mentioned above聴longer tent life from lower UV exposure. The challenge is how to do this effectively. And the solution is, I really don’t know. If some trees are in the area, then theoretically you could tie a tarp out to several trunks, centering it above the tent. That would be the lightest solution (you don’t say whether this is an issue when car camping or backpacking or canoeing, so I’m not sure whether weight matters).
Alternatively, and if weight isn’t a real issue, you could pack one of the new generation of tensile tarps, which are semi-freestanding. MSR’s 12-foot Parawing ($140) would, I believe, be large enough to fit over your Roadrunner. It would add about three pounds to your load, but seeing as the fly on the Roadrunner weighs a pound or more, the net weight gain wouldn’t be that great. And the comfort gained would, in my view, be enormous聴better ventilation, good rain protection, and more.