This is a many-layered question!
First, I want to correct a wrong impression which is entirely natural for someone who doesn't know the details of physical theory, and which isn't specific to gravitation. It's the idea that all the gravitons are shooting off into hyperspace, where they might get lost, build up in numbers, and so on. This actually would apply to some gravitons, but the wrong impression is that gravitation in general involves such a process.
But it's even simpler if we just talk about the electric field associated to an electron. We all learn that electricity, magnetism, and light are all aspects of the same thing - the electromagnetic field - and that photons are the quanta of electromagnetism. So does that mean that an electron, or any particle with an electric field, is emitting an unending stream of photons? That should sound problematic because the photons should carry energy and this would violate conservation of energy.
One of the peculiar concepts of quantum mechanics as applied to fields - so, quantum field theory - is that of the "virtual particle". It's bound up with the fact that quantum mechanics deals in probabilities and uncertain outcomes. For a technical discussion previously held on this forum, see
https://www.physicsforums.com/showthread.php?t=482956", especially the link to
Arnold Neumaier's FAQ... but if I can just jump to the conclusion, a static electric field of a single particle does not consist of photons streaming into the vacuum never to return, it consists of virtual photons which only have a conditional existence - at least by the usual empiricist or operational standards of reality used in quantum physics. If there was another charged object there, which could "measure" or otherwise be influenced by that electric field, then these virtual photons would get to show up indirectly, because there would be observable, quantitative changes in the motion of both the electron source of the field and the second object which the field was acting upon, which could be understood (in a particle picture) as being due to the exchange of virtual photons between the two objects.
But a photon only gets to be real - again, by these same pragmatic standards of reality - if it actually goes on to lead an independent existence from objects that emit it or absorb it. For example, if an electron undergoes accelerated motion - e.g. moving in a circle - then classically it will generate electromagnetic waves, and quantum mechanically this means that it is emitting "real" photons.
This is a potentially paradoxical distinction, because it may seem that a photon is virtual only if it gets reabsorbed before a measurement is made, and surely our "real" photon, streaming away into space, will eventually get absorbed by something; yet this absorption can't retrospectively make its existence unreal. The distinction between virtual and real photon might seem like an unnecessary obfuscation - it's virtual if it was absorbed before you could measure it directly, it's real otherwise. But in fact there's an issue here which is fundamental to the way that probability works in quantum mechanics, at least in the "sum over histories" version of the theory. One of the phenomena which makes quantum probability different to ordinary probability, is that different possibilities can "cancel": for example, in the famous double-slit experiment, the dark regions are explained as being dark because there are two paths for the photon to arrive at the dark region, but their "probability amplitudes" cancel. This does not make sense in terms of ordinary probability: if there are two ways that something can happen, it never means that in total, it becomes
less likely to occur! But something analogous does, nonetheless, occur in quantum theory - but it can only occur if the different "histories" don't leave undeniable traces of their existence by interacting with something external. If they do, they "decohere" and the "destructive interference" of quantum probabilities, in which multiple possibilities can mutually cancel each other, cannot occur.
You may think that doesn't make sense and I would actually agree. If, in explaining to ourselves what quantum theory means, we have to abuse the concept of probability like this, it does mean that we don't understand its ultimate truth, not that probability has "counterintuitive" properties. Nonetheless, this picture of quantum theory is probably the most intuitive one we have, because it allows us to visualize physical processes. They are "random", but it's a strange form of randomness where probabilities can cancel. And though it is ultimately a little illogical, we do have very precise methods for calculating those probabilities, and they give us the correct answers experimentally, so one has to give the picture a little respect, even if it can't be the very last word about the nature of reality.
Returning from the wilderness of quantum ontology, what I wanted to do was to correct the idea that the existence of a gravitational field, or of an electric field, consists of a stream of "real" particles (or strings) radiating into the void. A static field, if it is to be understood in terms of particles (or strings) is to be understood as a standing probability distribution of virtual photons (or gravitons). You can certainly have a real photon or graviton that is actually radiating away into space, but it will have to be generated by a motion on the part of the source of the field.
So if we finally switch to thinking about the gravitational interactions of braneworlds in hyperspace, the very first point is that the gravitons, the closed strings which mediate their gravitational interaction, will be virtual, unless they are generated by motion at the source, in which case they will be gravitational waves. Gravitational waves appear to be a real phenomenon - there is a famous binary pulsar whose two members are slowly spiralling in towards each other, and this change of motion is attributed to gravitational energy being radiated away. But to a first approximation, if the braneworlds act gravitationally upon each other, it will be because of their static gravitational fields, which (analysed in terms of individual particles or strings) are made of virtual gravitons which aren't leaking into the hyperspace between the braneworlds and building up - only the "real" gravitons can do that.
So that's the very very first thing to say in response to your question. It's all really just a prelude to tackling it seriously, using the theories we have. Any string cosmologist who was going to think about explaining dark energy in terms of braneworld gravitational radiation or gravitational interactions would already know these distinctions (real versus virtual) because they are basic to quantum field theory, which (from a string perspective) is the approximation to string theory which treats the strings as zero-length point particles. With that prelude out of the way, we can really start to address the question, and of course here it becomes extremely challenging, because we are dealing with incomplete, highly speculative theories. Nonetheless, I'm quite sure something like this idea has been articulated, and I will attempt in a subsequent reply to say something about it. But that will have to wait for tomorrow.