So here's an example of what objective analysis looks like:
https://anydice.com/program/32408Your average damage right now is almost 29 on a normal hit and almost 44 on a crit, thanks to Savage Attacker. If you didn't have Savage Attacker, it would be a bit over 27 on a non-crit and roughly 41.5 on a crit, so Savage attacker is adding +2 to +2.5 average damage. You have at least +12 to hit, and advantage against large enemies, meaning you should hit a target with 19 AC like the one we're talking about 91% of the time (more if you have other bonuses I'm not seeing), and you should crit with advantage and a crit range of 16+ (25% as you put it) 43.75% of the time, thanks to all the effort you put into it.
That means your average damage per hit against the target we're discussing is 0 * .09 (Misses, dealing 0 damage) + 44 * .44 (crits) + 29 * .47 (normal attacks) = 0 + 19.5 + 14 = 33.5, rounding up in ways that are strictly favorable to your setup at every turn. On average, it takes you 15 attacks against it to kill it with your fighter set up in the way you have displayed. Given your 9 attacks in the first round will on average deal 301.5 damage, most of the time you need an extra 218 damage from other sources to finish him off.
Meanwhile, if you were using the elixir which grants 27 Str and were using Great Weapon Master instead of Savage Attacker, you would be dealing a bit over 41 damage on a non-crit, and a bit over 55.5 damage on a crit. This is driven by the extra 4 damage from the Str elixir and the extra 10 damage from GWM. You would have 1 less to hit, since you would get +4 to hit from the elixir and -5 from Great Weapon Master, and would crit on 17+ instead of 16+. This would mean in turn you would miss 12.25% of the time instead of 9%, and would crit 36% of the time instead of 43.75%. However, because getting much higher damage when you do crit at some point offers much better returns than improving your chance of a crit in the first place, and because Great Weapon Master is just much stronger than Savage Attacker, you would be doing significantly more average damage.
Against the target we're discussing your average damage per hit is 0 * .14 (misses) + 55.5 * .36 (crits) + 41 * .5 (normal attacks) = 0 + 20 + 20.5 = 40.5, rounding in ways that are generally unfavorable throughout. That's 7 more average damage per attack, or about 20% higher average damage, meaning on average it takes you 12 attacks to hill it with your fighter set up in this way, 12.34 to be more accurate. Of a note though less than 2% of the time do you fail to get a crit in the first round and thus you get 10 attacks in round 1 98+% of the time thanks to Great Weapon Master, so you're dealing over 404 average damage in round 1, leaving just an extra 114 damage to finish him off.
So how do I know that Great Weapon Master is stronger than Savage Attacker, and the Strength elixir is a better option for the character as described than the crit elixir? Because the numbers say so. Because I can proclaim with confidence that 100 different people could do this fight 10x each with your setup and 10x each with mine, and *all of them* would have better average results with my setup than with yours. That doesn't mean that even with the elixir and feat swap outs we've arrived at anything even close to an optimal setup of course. You can do better than this, much better, if you're not a Fighter 12. That's entirely ignoring how weak he is to hold monster and thus the superior options you have with a well designed party. But I don't rely on just how it feels to me as I run through it once. I don't just look at something that worked and assume it's the best option and everything else is trash. I can compare what sort of outcomes are expected with tweaks to the setup and see which one will be more favorable, and determine with absolute confidence that one is better, *and I can then back it up if questioned on it*.
