"I'm a monist about mass-energy, .. What is the subject of your monism?": I too am an energy monist. I am a strong atheist, so I am not into Gods. The subject of my monism is 'truth'. I have already proceeded as far as was possible. Now I wait for science to gather more data.
"I'm attracted to my hypothesis for the very reason that it doesn't require phases, doesn't require true non-existence at any point - that is, time exists because mass-energy does, not vice versa.": If it does not require phases, then how does it explain the first appearance of energy or 'what exists'? Mass-energy, space and time, all are related. One is not without the others.
"On our present understanding, no, energy doesn't flit between existence and non-existence. Instead there are no extant counterexamples to the principle that energy is indestructible, can neither be created nor destroyed.": We do know what 'virtual particles' do. Non-existence does not mean destruction of energy (it is a sort of subsidence of energy). Energy can appear again with space and time.
"But if time is a property of mass-energy, then there's no question of 'beginning to exist'. Mass-energy is, therefore spacetime is. Before time was, I AM, says mass-energy ex hypothesis.": The Trinity, as I stated above. Phases, subside and appear again together. A cycle like in Hindu concept of creation and dissolution, or continuous creation and dissolution in Multiverse scenarios. I don't know.
"So they're offering hypotheses, but not supporting them, ..": In their time (around 1,000 BCE), there was not much they could offer as evidence. It was the best they could stretch their thinking to. Even now, we can not offer anything more than that - monism. They were our monist predecessors.
"Is it real? If so, why is a coherent perturbation in it, such as you say we each are, not an aspect, an element, of reality? And if the existence of physical objects is not real, what is it instead? After all (going back to Berkeley) they're still there when there's no one around, that is, they have objective existence.": The perturbation is real. It is a inherent property of energy. Coherent perturbation - that is a good point. I think it is something like agglutination, forming of a set, like in a human body; or the building, lawns and trees of Berkeley. The Sets persist and do not require any one to be around. Living or dead, I would have the same appearance till this set is broken and the constituents become the part of a new set/sets - Chemical recycling.
".. Which seems an odd way to regard the manifest reality ..": The reality is not manifest, it is hidden and difficult to realize. What we perceive is only subjective, an illusion, 'maya', which is dictated by evolution.
"How do you know? .. We're biochemical / bioelectrical patterns that form in parts of what exists. When those parts irreversibly cease to maintain the pattern, we die. The parts are recyclable, nothing (if we put Star Trek beaming to one side) suggests the pattern is.": Even after I am dead, every atoms of my body will be kicking and frolicking. That never stops. The perturbations will continue for ever. I am not a believer of rebirth/reincarnation. Call it dying or call it change of form. Krishna said in Gita:
BG 2.12: Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be.
BG 2.17: That which pervades the entire body you should know to be indestructible. No one is able to destroy that imperishable.
BG 2.22: As a person puts on new garments, giving up old ones, it similarly accepts new material bodies, giving up the old and useless ones.
(If you try to find Gita translations on internet, you would find the mention of the Supreme God or soul, but in orginal Sanskrit verses, these are not always mentioned. These are interpolations by theist translators)
"Spaces in what, exactly?": The volumes (dimensions, coordinates) that I fill in past, present and future. It is the perturbations in these volumes that gives rise to the false feeling that Aupmanyav exists.
"And what do you say "I" is here? (For me, "I" is my sense of self, generated by the patterns in my biochemical brain, the "I" who looks out through my eyes.)": This 'I' 'who looks through my eyes' is only an illusion. There is no real 'I' other than 'what exists, physical energy'. The rest, as you said, is generated by the patterns in our biological brain. I do not believe in existence of 'soul'.
"I think we already have. The absolute truth is expressed as, There are no absolute truths outside this sentence.": Well, you are welcome to your views. I think we still have to find the answer to the mystery of the Trinity - Energy, Space and Time.