Word to mean "iterations that are different"
Solution 1:
Although incantations is incorrect in this context, incarnations (a concrete or actual form of a quality or concept) would have been perfectly valid. I think in some ways it could be better than revisions/iterations, since it implies each new version was a complete "rebirth", rather than a (possibly minor) variation on the previous one.
Here are several hundred written instances of "went through several incarnations", many of which are very similar to OP's context. A typical one being...
The 4-inch-bore and 5-inch-stroke engine went through several incarnations as IHC struggled to get its problems resolved.
It really depends on whether OP wants to convey the impression that each different version was an incremental improvement on the previous version (in which case iterations works best), or that radical changes and redesigns were involved (in which case I think incarnations works best).
Solution 2:
Iterations is the right word here, unless they were completely different. Iterations bear similarity between each other but are rarely identical. (In programming, iterations of a loop that runs a finite state machine are very different from each other in all parts that matter.)
Otherwise, it could be said the experiment went through several approaches, where the approach to the result was totally changed each time.
Solution 3:
How about the experiment went through several revisions prior to the final design?
(Or you could also just as easily say that the experiment went through several changes or variations as alternatives to that too)
Solution 4:
Try permutations. It implies a set of items in which each one is derived from an initial state with a specific change.
Solution 5:
if the experiment was constantly changing, how about using "evolutions"