Off topic a bit, the Japanese name of Black Omen happens to read as KURONOYUME(クロノユメ). although it has nothing to to with Crono or Chrono(KURONO) at all.
Back to topic, doesn't dream stone has something to do with Lavos? I don't know, but they did have some similarities, first of all, dreamstone is red, as well as the Frozen Flame which is a fragment from Lavos, the Masamune sword which is made from dreamstone has some kind of sentience to his user's spirit power, while the Frozen Flame can make contact with Lavos itself.
The connection between Dreamstone and the Frozen Flame has never really been touched on in depth. Dreamstone existed before the Frozen Flame and Lavos landed, yet it seems to be a perfect conductor for his energy.
Zergplex, your hypothesis makes a lot of sense; I really like it. A few questions are raised, though. If the MM has a dream entity manifestation, why is that entity identical in appearance to its physical counterpart (or at least the counterpart in its better days...), while all other examples of dream entities have manifestations that are clearly different from the objects they occupy? Could it be that Melchior actually had a great deal of control over the kind of dream entity that was produced, and was able to literally program a dream creature like a machine? It starts to get a little far-fetched at this point, but not when you consider CC's convoluted storyline, I suppose...
For the reason the Dream Mammon Machine looks identical to the original Mammon Machine you need to look at Melchior's design. I don't believe anything he crafted was a coincidence, the spirits formed within the artifacts have just as much purpose as the items they are connected to.
Case study 1: The Masamune
The Masamune is powerful blade which grows in power from the inner strength of the wielder. The true strength of the Masamune comes from the soul of the wielder, this concept is key to understanging Masa and Mune.
Masa and Mune were designed with two perogatives in mind. The first was to protect the Masamune until a worthy person comes to claim it. The second was to provide companionship and direction to the wielder of the blade, to help him find his inner strength and awaken the true power hidden within the blade.
Masa and Mune's personalities show courage, intelligence (to a point), and an understanding of what it means to be a hero. They were to be the spiritual guides to the owner of the blade.
Case Study 2: The Pendant
The pendant's original design goal was never stated, but I feel it could be implied. I feel it's original purpose was to aid in interfacing with the the artifacts of Zeal, to aid in the activation and control of the Mammon Machine, and possibly to amplify magical power. As the Pendants design goals had multiple layers, the spirit within as well.
Doreen was designed to compliment both the usages of the pendant, but also to compliment the
user of the pendant. The pendant was crafted for the royal family of Zeal, and Doreen's talents were designed with this in mind. As such Doreen has a sharper mind then her siblings, and is well versed in philosophy as we see during Chrono Trigger. She appears to be more mature and serious then her siblings as well. All these facts point to her role being as an adviser to the owner of the pendant. Doreen's design goal was to advise the owner of the pendant so that it's power would not be misused.
Case Study 3: The Mammon Machine
The Mammon Machine was crafted from Dreamstone to draw energy from a powerful new source the guru's had identified (they we later realize is Lavos). The Machine radiates the energy from the actual mechanical shell, but it must be drawing the power from Lavos somehow.
The Mammon Machine spirit was designed to be the second end of the machine, to draw the power from Lavos itself and shunt that energy to the physical side of the machine in Zeal. The spirit was formed to resemble the physical Mammon Machine because it was providing the same function but in reverse (absorbing Lavos's energy rather then radiating it out).
Unlike Masa, Mune, and Doreen the Mammon Machine's spirit didn't require a complex mind to complete it's job, so Melchior chose not to give it a full mind. It understood the workings of it's job, and the basics of defending itself.
In short I feel all the dream entities were formed by Melchior's dreams to fulfill a purpose. Their forms and personalities are clues to what that purpose was going to be during the time of ancient zeal, and what their purpose could be today.