Many, many members on TFF have reported that removal of 1/3 of the media (this is the main biomedia portion of the media) poses little chance of spikes or other problems in the donating aquarium. Regardless of whether you need to take scissors to an established sponge or just purchase some new loose media for the donating filter and then divide up some loose media from one or more trays, this 1/3 transfer is by far the top choice for removing weeks off the fishless cycle of the new tank.
As far as *purposely* fish-in cycling a new tank, I feel this is the domain of very experienced retired aquarists or planted tank enthusiasts, both of whom, we'll generalize, have time and inclination to putter with the tank each day, including making daily water changes if necessary. This is not generally the realm of beginners or people working long hours and tired when they get home would be my guess. Anybody who's been through the tyranny of trying to keep a fish-in cycling tank below 0.25ppm trace levels knows what an extreme pain it can be (or, of course, they're not measuring, in which case its the fish, presumably, who are feeling the exteme pain.)
So to me it seems a no-brainer to choose the current state-of-the-art method and tranfer 1/3 of the biomedia, followed by verification that said biofilter has "taken" within the hardware of its new home by performing a fishless cycling procedure. A fishless cycling procedure on a 1/3 mature media transfer will most likely be just the "qualifying week" where you watch 5ppm of household ammonia drop to zero ppm ammonia and zero ppm nitrite in 12 hours or less for the entire week -- this is just such a reliable way to actually know that the biofilter will do a great job that its hard to imagine people not bothering to do it these days. To not do it is just to be left to a guess as to whether the biofilter is working properly yet.
As far as the tools to carry out the biofilter verification process, truck, you are such a good planted enthusiast and fishkeeper that it mystifies why you get so hung up on the variability of the accuracy of various test kits. Accuracy really doesn't need to take a top spot in this sort of process if its carried out properly. Its usually more about the crude but frequent and redundant recording simple results to get a little verification of a process you know the outline of. For instance, the multiday back and forth of green, yellow, green, yellow of an API ammonia test result is more important than necessarily knowing whether the green was 1.0 or 3.0 or 5.0 when you happened to take it (granted of course that we hope to avoid the really dark greens that might indicate 8.0) The chemicals that make up these kits are just not that complicated. They will be "good enough" the vast majority of the time and the process itself will expose the occasional bad kit, I feel.
Just having beginners exposed to the exchange of information about biofilters and fishless cycling *at all* is such a big thing.
Anyway, for GTS, I think the 1/3 MM move with household ammonia driven fishless cycling verification of biofilter function would by far be the top choice. If the parents just won't do that (which would be a shame) then the washing of the MM in the new tank while it is undergoing a fishless cycle would be a second choice, somewhat far down from the top choice. Then the other choices, gravel moving, running 2 filters for a while, etc. are all going to be way, way down from these top ones and not that different from the typical long fishless cycles we see here.
To me though, all these fishless cycle alternatives represent the simple idea of verifying the biofilter operation and thus knowing you've done your best to give these fish a clean, healthy environment prior to them coming to your home, so that they won't suffer even minor gill and nerve damage that you likely wouldn't have much way of knowing.
~~waterdrop~~