I had hoped that the Four Noble Truths, the Eight-fold path and Three Jewels would be workable with what I'd set out - what do you think? As for Nirvana, "enlightenment" could be considered the carrot at the end of one's various reincarnations, entry into the Elysian fields, a related realm to the Olympus/Heaven where the Gods reside. They'd need something alternate to the Pali Canon, a Greco-Buddhist canon of their own, but yeah...
Oh, okay. I misunderstood you, and thought that what you presented was the final product.
Well, to make it Buddhist, you probably need to keep the Four Noble Truths, Eightfold-Path, and Three Jewels. Anything else isn't distinctively Buddhism, though I won't argue what constitutes Buddhism and what doesn't. The thing about a divine afterlife being a goal, as opposed to Enlightenment, means this religion isn't that Buddhist. At least, it's hazy and arguable. I mean, yes, there's the Pure Land in regular Buddhism, but that's in a much more developed Mahayana Buddhism, whereas I think Greco-Buddhism was less developed. So, instead, you can have enlightenment still as a goal, only with the Pure Land. People live their lives, then go to the Pure Land/Olympus if they're good enough (or if they call upon the powers of the Amida Buddha, or Sakyamuni, or whatever you want). Then, they'll live there as long as they want, then realize become enlightened, so ultimately all good souls disappear, while the bad souls either suffer forever or suffer until their karma disappears and they too disappear.
You can probably preserve the Eightfold-Path completely. It just needs a new spin. As for the Four Noble Truths, you can just create new ones, because I'm not sure I would call this religion a type or extension of Buddhism. The Three Jewels are the Buddha, Dharma, and Sangha. Since you seems to be creating a new religion, not a new type of Buddhism, you can probably use your version of the Buddha and Dharma instead, while reinterpreting the Sangha to mean the community of Economidarmists.
The thing is, I'm pretty sure the Greco-Buddhists used the Sanskrit canon, but I could be wrong, so you might want to look into that. If you use Sanskrit as a liturgical language and the Sanskrit Canon as your canon, your religion would look a lot more like Buddhism.
Or, this is another option: The Three Jewels are the
Buddharaja, or Buddha-King in this scenario, the
Dharma-Maat, the Truth of the Universe and the teachings/way of the Buddha-King, and the
Sangha-Dynastic Cult is the organization of Economidarmists on Earth.
Many ideas can work. Buddhism is pretty flexible. You can probably create a fantastically complicated world-view from it.