So couple questions about this and the study you did:
Did you account for cards such as Zapp being played?
Is the minion stats of board accounted for throughout the rounds? As your board is typically much larger than your Baron, that means that they can sometimes tank extra hits whereas Baron is a small, weak-statted minion by the time he gets played and dies in 1 hit. To account for this, do you have statistics on how often your Baron, or other "key cards" are attacked first? Dying first is very easily skewable in that comparison.
Going back to your current metric of first to die - Baron being compared to Juggler, and to an extent mechano, is an iffy comparison. They go in different builds. Juggler survives to be a later minion alive with your analysis, sure, but if you think about how a juggler demon builds, that makes more sense that their board will be thinner, especially as voidlord is a common tool for jugglers. By the time that voidlord and all its spawned taunts die, your board is going to be down to less minions (4-5) on board by the time that Juggler can even be hit. Baron is more often played with beast or mech comps (more beast), where they don't have returning taunts. So once your first taunt is down, everything is immediately open, Baron immediately vulnerable. Mech builds are fairly similar to beasts in this way that they typically don't have returning taunts, once their initial ones are gone. Though it's thrown off more by divine shields. Mechano and Baron both in mechs are comparable, mostly, when used in mech comps, but not other comps. If you have them both on board in any of your games, you'll have to account for that, your board positioning, and cleave. As baron usually goes further back, closer to taunt, and more readily cleaved. So other things to consider with your program would be to account for cleave and how often that impacts your results as well as what comp it is being played in. If you have Baron and Juggler (or mechano) on board, which dies first more often? If you have Baron in a juggle demon comp instead of Juggler, does baron die noticeably more often?
Very interesting preliminary research and statistics though, has me curious for sure. Makes me want to see further data on this for sure! Some of those things I mentioned above I think would be particularly interesting to see accounted for in data because otherwise, currently, the data is interesting but has enough potential holes and confounding factors for me to consider it proof of non-RNG being used (yes, it is significant as of now, just not sure it's necessarily telling).