What led me to this site was having a theory similar to what your post entails but I took it a little further. In Revenge of the Sith, Palpatine manipulates Anakin at the theater event and tells him a story about a "Wise and powerful" Sith "Darth Plagueis who discovered the secret to immortality - 'keeping the ones he loved from dying'. Typical in any manipulation there's bound to be some ounce of truth to stitch it together, and the only way that Palpatine would have had such familiarity with Plagueis is if that was his master and that 'he' had killed him in his sleep, where he grins in reflection.
Palpatine also reveals that his master taught him everything he knew in another scene. Apart from any canon, Plagueis sounds like he lived a very long time ago compared to current events in episode III. If this were true, Palpatine very likely was using the darkside itself vs some apparatus to present a false image publicly, filling peoples minds with an illusion. He would be so disfigured after battling with Mace, compared to any of his apprentices because he could literally be 500 years old. That he was so committed to the darkside that he cheated any pitfalls associated with it. He also shows high enthusiasm when he finally meets Yoda, which likely is rooted to his self image of long existence - not exactly life as Yoda was also long living. Thus seeing the other as a kind of distorted equal.
He was also still vibrant when he quotes - "Unlimited power" and destroys Mace. The power probably extends beyond the scope of just force lightning. Rather the ability to continue living - albeit disfigured from age, more zombie esque. The darkside would have concealed his true age and Sith qualities, but like you said, he was so manipulative that he simply allowed his true appearance to take shape in front of Anakin. Afterward he took advantage of it publicly, seeing no reason to hide anymore, moreover after issuing order 66.
A secondary question that arises is why did Darth Vader physically age at least twice as fast as he should have, being so young when he was converted? As he is revealed without his helmet, apart from scarring, he already appears old - up until this point he had not begun the journey back to the light side per his interactions with Luke - where it would be suggested that his aging was due to a lack of commitment to the darkside, this being contrary to Palpatine who cheated death and would have been truly very old.
Another thought is that perhaps part of acquiring the long life Palpatine could have been draining life from another such as his loyal apprentice Darth Vader - where he celebrates in episode III that his new apprentice is "Far younger and more powerful", even to the extent that the darkside would drain from that greater power in Anakin.
Finally, I've always imagined that Palpatine told Anakin the story of Plagueis because he was actually boasting on how he himself used the knowledge to order the midi-chlorines to create Anakin in the first place - truly "owning" him. This event could have taken place a century prior and the force determined the arrival and timing of the child - along with presented prophecy from the Jedi temple.
As to the more recent blundered episodes 7, 8, & 9, which I fail to recognize and didn't watch the last installment, I understand that Rey is revealed to be Palpatine's grand daughter but if the theory that he's 500 years old held up, that would seriously undermine Rey's identity and the entire storyline. It also seemed odd that at any time the Sith lord would have embraced marriage or having a child which is the essence of life not death. Even if the story claims he killed off Rey's parents, - his own child, later.