Your insight about forces carried by massless vs. massive particles and their respective ranges is absolutely correct. Congratulations!
(Now, I'm wondering if this particular idea implies that since gravity's range is infinite, that implies that if gravity is transmitted by force-particles rather than space-curvature (assuming that that's a distinction with meaning), then the virtual gravity force-carrying particles have to be able to have arbitrarily small energies, and thus no significant rest mass...)
It is generally agreed that the still-to-be-constructed theory of quantum gravity will have gravitons, particles carrying the gravitational force analogous to photons for the EM field, and yes, gravitons should be massless as you argue. This is not however in conflict with the description of gravity as space-time geometry. Though the full details will have to wait till we understand quantum gravity completely, provisionally we can make unambiguous sense of gravitons at the pertrubative level: Think of a gravitational wave as a small ripple in spacetime, then one can quantize this perturbation and gravitons are to the wave as photons are to classical EM waves.
I recently flipped through the "Cartoon Guide to Physics", expecting an easy-to-understand rehash of ideas I was long familiar with; and that's what I got - right up to the last few pages, where I was presented with a fairly fundamental concept that's been absent from the popular science media I've enjoyed over the years. (Specifically, that the uncertainty principle, when expressed as linking energy and time, explains what electromagnetic fields actually /are/, as the propensity for virtual photons of various strengths to happen.) I find myself happy to try to integrate this new understanding - and at least mildly disturbed that I'd been missing it for so long, and with an increased curiosity about how I might find any other such gaps in my understanding of how the universe works.
So: what's the biggest, or most surprising, or most interesting concept /you/ have learned of, after you'd already gotten a handle on the basics?