....FYI:
http://www.swingpaints.com/1802us_can.htm
from the Circa 1850 website: "Circa 1850 Tung Oil is a ready to use finish made with raw tung oil, and does not contain any other oils, resins or varnish."
I got some raw tung oil from Lee Valley some years ago to use for bowls and some utensils that I made. The raw UNTHINNED tung oil is thicker than raw linseed and BLO that you have in those other two bottles. So clearly Circa 1850 at the very least adds some thinning solvent to stretch the use of the rather thick raw tung oil.
Also as I understand these things from my wood working hobby linseed oil has not been "boiled" to modify it to dry sooner for many, many decades. Quite possibly not since the turn of the 1900's. Instead driers have been used to avoid the serious risk of fire and explosion that goes along with correctly boiling the oil.
Speaking of driers there's a high likelihood of finding driers in the Circa 1850 stuff as well. The truly raw tung oil that is rated for food utensils has NO driers in it. The downside becomes the long drying/polymerizing period that goes along with this. Overnight won't do it. In the hot sun for 5 to 6 days may well do it nicely thanks to the heat and UV radiation. But indoors? Truly raw tung oil takes about two weeks before it loses the "oily" feel to the touch. You say you didn't feel this by the next day even in the case of the raw linseed. That only tells me that you don't know what you're looking for in terms of "wet oil" signs because raw linseed oil takes literally a couple of months or more before it fully polymerizes from contact with heat, light and oxygen. It most certainly will not be in any manner dry after a few days.
One major hint to work with is the smell of the finish. There's a noticeable change in odor as the oil moves from being a liquid to fully polymerized. Then once fully polymerized for long enough it no longer smells at all. It would likely not be a bad thing to use that "no smell" test as an indicator that it's time for a feeder coat of the same oil as originally used if one wants to freshen up the protective aspect of the wood.
A few other things.
You mentioned putting the wood in a bag with some silica packs to see if the wood "dried out". What do you expect to happen to the samples from this? The silica will absorb SOME of the water from the wood but not all of it. Wood moisture doesn't work that way. Also you're using reasonably dry wood already so the other aspect of it simply shrinking too much and splitting isn't going to occur even with the silica packs in the bags. If you're thinking that "dry rot" will occur if the wood is dry enough then you're mistaken again. "Dry rot" still requires a specific amount of moisture to be present so that the various fungi that affect wood can grow and feed on the cellulose of the wood. And if a gun safe was that humid then it's a sure thing that the steels would be rusting.
So all in all you're off to a rocky start. I'm truly not trying to rain on your parade. If the rapid dumping of what I've learned about oil finishing sounds that way it's only because I'm already accused of being wordy and smothering the stuff above with friendly platitudes would make it that much worse....

In reality you're doing a great job. It's just that you need to modify your testing into something a bit more long term..... just like an oil finish is. Oil finishing isn't the best option for those afflicted with ADD...
Since it's summer you can use the hot sun to speed up the process. I'd suggest you just set your rapidly recoated samples out in the sun for a couple of days. Monitor the odor of each two or three times a day and you'll find the odor changing as the light, heat and oxygen modify the liquid oils first into a sticky gum and then into a solid film down in the pores of the wood.
Note that the odor of the tung oil finish you're using may fool you when first applied. It'll take a few hours for the apparent thinners in the oil to evaporate to leave the oil and driers only. So monitor the odor to find out when it changes over to a sort of sweeter smell.
None of these oils "dry" like you get with some paints. Instead once the thinners are gone, if there are any, then the oil reacts with UV and oxygen to modify the structure. This being the process of "polymerization". The driers that are likely found in the Circa 1850 are more about speeding up this process than actually causing it. In a way the driers are sort of like a catalyst in polyester resin. The resin will cure on it's own given enough time. Those of us that have had to toss out a lumpy or solid bottle of the stuff can attest to that.
In terms of protection from handling and the elements I'd suggest a two prong test.
First is to see if the oil finish can make a rub line from a pressure point less damaging. You'd need to arrange something that presses on the wood with an identical force and a well rounded and dulled nail for the test. Then perhaps do the same with a scratching nail.
Second is the ever popular water resistance. The ability to make the water bead up instead of sheeting over the surface is a key element in avoiding any water soaking into the wood. A mister used on the sample blocks can be the "test". For this you'd want to let the oils harden up for something like a month or so. By that time if they get some sun tanning time they'll be as polymerized as they are going to get. Mist on some water and simply confirm if the water sheets or beads. It's as simple as that. Beads are good because it means the water was denied possible entry to the wood and that the oil finish isn't able to bond to the water.
From there shower the samples for an hour. Dry and let sit to dry for a good two hours then mist the samples again. Mark down whether they sheet the water or not. Repeat the shower, drying and testing.
After some amount of showerings even the best oil finish will be damaged enough that it allows the water to sheet on the surface instead of beading. And that is a sign that the oil finish has been compromised in some way and that unwanted water being soaked into the wood is not far behind. It's also the sign on my own oil finished long guns that get used in bad weather that it's time for a feeder coat of oil.
Keep in mind the old wood finisher's credo about oil finishes. Simply put you are NEVER finished. In the classic times when we didn't have all the miracle solutions of today as supplied by chemistry the method was "One coat a day for a week. One coat a week for a month. One coat a month for a year. One coat a year for ever after.". And this applied to furniture kept indoors out of the rain. An oil finished rifle stock can require re-coating two or possibly three times a year. In particular out here in the Great North"Wet" side of Canada.....
