Do you need to be able to edit the data on the left side of the grey column? If not, then I might have a regular formula solution.
First, I turned on iterative calculation with max iteration of one. This should only be applied to formulas that are using iterative calculations. It won't impact your other formulas.
Next, I converted your script into the formula equivelant. All of your script's setValues arrays are compressed and stored as the dropdown storage cell, E4. There are three storage options. A reset option to revert back to the original sample data, an option to step forward an iteration, identified with the green dot. Finally, there's the option that was stored last round.
After selecting the next toLoad value in T2, use the dropdown storage and select the option below the label with the green dot. Each table has a formula near the top left cell that spills the table/value.
Most importantly, undo only requires one click in this setup to reverse the last round of changes.
Here is the spreadsheet that includes the formulas. Let me know if you have any questions.