I suggest a common sense solution of this is simply that aggregates may refer to the "unenlightened aggregates" and "unenlightened aggregates". Enlightened aggregates are something like what was taught by the Buddha to Bahiya:
http://www.accesstoinsight.org/tipitaka ... .than.html"Then, Bahiya, you should train yourself thus: In reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. That is how you should train yourself. When for you there will be only the seen in reference to the seen, only the heard in reference to the heard, only the sensed in reference to the sensed, only the cognized in reference to the cognized, then, Bahiya, there is no you in terms of that. When there is no you in terms of that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress."
Through hearing this brief explanation of the Dhamma from the Blessed One, the mind of Bahiya of the Bark-cloth right then and there was released from the effluents through lack of clinging/sustenance. Having exhorted Bahiya of the Bark-cloth with this brief explanation of the Dhamma, the Blessed One left.
The unenlightened aggregates are the source of dukkha, or better said are dukkha, because there is of course no dukkha apart from the aggregates.
In practical sense most of us don't recognize dukkha most of the time, because it is the default state - the background to our experience. The Buddha likened this to the leper enjoying cauterising his body over the pit of glowing embers:
http://www.accesstoinsight.org/tipitaka ... .than.html"Now suppose that there was a leper covered with sores & infections, devoured by worms, picking the scabs off the openings of his wounds with his nails, cauterizing his body over a pit of glowing embers. The more he cauterized his body over the pit of glowing embers, the more disgusting, foul-smelling, & putrid the openings of his wounds would become, and yet he would feel a modicum of enjoyment & satisfaction because of the itchiness of his wounds. In the same way, beings not free from passion for sensual pleasures — devoured by sensual craving, burning with sensual fever — indulge in sensual pleasures. The more they indulge in sensual pleasures, the more their sensual craving increases and the more they burn with sensual fever, and yet they feel a modicum of enjoyment & satisfaction dependent on the five strings of sensuality.
But once cured, this would of course be a source of pain.
I think we should be careful in disentangling ourselves from attachments and cravings lest we replace them with aversion for the people and the world. Saying that "the world is suffering" carries a massive emotional connotation. Equanimity is the right attitude, not aversion or indifference.
PS Thank you for posting the passage above, Prasadaccita! Here's the link to Ven Thanissaro's translation:
http://www.accesstoinsight.org/tipitaka ... .than.html