I'd dispute that a theory is "a well tested model." A theory is a TESTABLE hypothesis.
If something isn't testable, it isn't a hypothesis. At best it is speculation or conjecture.
When a hypothesis has been repeatedly tested and shown to produce consistent results, it becomes a theory.
Theories are then subject to constant refinement or revision on the basis of further hypotheses and experiments.
The Stone Tape Theory is not a theory in any scientific sense. It is a hand waving argument, a conjecture, wild speculation, or an "explanation by fanciful analogy".
In order to become a theory, its proponents would need to put forward some consistent definitions, and come up with some repeatable experiments.
1) What is "emotional energy" and how is it measured and categorised?
2) How is the information encoded and stored in the stones (or other media)?
3) How is the information extracted, received and experienced?
There are so many holes in the idea.
1) Why is it that certain emotions seem to be "recorded" more often than others? No one ever sees a ghost of two happy young lovers having a picnic. No one sees a ghost of a couple having a passionate sexual encounter. No one sees a ghost of someone angrily reprimanding a lazy servant. No on hears a ghost of a domestic argument. It always seems to be murder, suicide, execution, despair, unrequited love, or something totally unemotional like a Roman legion marching along the Great North Road.
2) If the walls of a haunted house are made of many stones, not all of which have their structure aligned the same way, is it that just one stone records the information? If not, why don't so many stones record it that the information that is transmitted back to the witness as a hopless jumble of out of phase signals? Why is it not overwritten by later events? What is the half life of the stored signal? How is it affected by changing moisture levels in the rocks, or thermal expansion and contraction?
3) Are the stone broadcasting the information all the time? If so, why don't they run out of "energy"? if not, do they somehow detect the "sensitive" witness and start broadcasting to them? Why do we get so few (no) reports of sensitive witnesses returning to a scene and seeing exactly the same thing time after time?
It is like one of those scam medical or cosmetic adverts: a few scientific-sounding terms, a tenuous analogy to something everyone can understand (a photographic plate, or a magnetic tape) and wishful thinking.