In practice, I don’t want this glass to be entirely invisible, but changes to that effect only worsen the issue. The .blend pictured above is attached.
1). Follow the Blender wiki instructions here, this will guide you on creating a glass shader with a transparent shadow.
2). Enable the ‘Multiple Importance Sampling’ option on the lamps and set the ‘filter glossy’ option to 0.20 or above. The MIS checkbox will allow the lamps to produce caustics which is the light rays refracting through the glass to give a realistic lighting effect. The ‘filter glossy’ option will also help due to an operation is does to make those light paths easier to find.
It seems odd that I should have this problem with Cycles; I expected that using a physics-based shader would result in a notable increase realism when simulating glass with such distinct refraction, reflection, and transmission characteristics. Did I read reference #1 that you provided, to say that to simulate glass properly in cycles, fundamentally, requires not just the Glass shader, but also a Transparent node? That, when I see light come through glass, it is because of its transmissive property, and the light coming through the glass shader is only delivered by a separate refractive characteristic? Isn’t all light transmitted through a substance either refracted or scattered?
Sorry to head off on a physics tangent, just trying to understand my mistake.
That’s why I mentioned the second option, each Blender lamp has a checkbox labeled ‘Multiple Importance Sampling’ in its lamp context (it’s off by default). Turn it on for both lamps and you should start seeing bright spots appear under the glass dome, this bright spots are the caustic samples that are now being taken.
In addition, the render context under the ‘Light Paths’ tab has a value box labeled ‘Filter Glossy’, Cycles being just a plain pathtracer means that caustic sampling is difficult by default, that handy little value then invokes a sampling technique that makes sampling those paths a lot easier and with proper falloff.
Use the clever method by Bassam Kurdali to get fake caustics, removing fireflies and reducing render time, while also solving the shadow issue. (http://urchn.org/post/fake-caustics-in-cycles)