Both of those sets are nice, using briarheart with high attack rate skills can be amusing, and I use Hexos in the archive from time to time when I want to go further. I'd recommend looking at the Tzogvin's set, for the bonus crit rate and crit damage, for situations when you don't need two defensive sets.

Yeah, the troll boss does hard lock one person, ruining solo runs. There is an overland set from summerset, Gryphon's Ferocity, which provides the same crit damage bonus, just without the crit chance, and that could be a good alternative. Dragonguard Elite is also an alternative for crit chance, just looking in scope of easy to access crit based sets to add damage while complimenting whichever set you go with for defense.

This is a hard question to answer. You don't mention your class for one thing. My other question is, what's your objective? To get through content as quickly as possible? For many players who are in ESO for the long haul, it becomes exactly that. Doing the same stuff over and over, only faster. Or is it that you can't solo certain things, e.g. certain world bosses? I'm struggling to think of something difficult when we limit ourselves to normal mode and cut out the dungeons where a mechanic prevents you from progressing. Where are you running into a limit with your current build?

I used to do what you do. Play solo. Find the one compromise build and call it a day, rather than adapting my build / playstyle to different encounters. Hexos Ward is a very good compromise until you've played for so long that you know most mechanics and, perhaps, some guild has coerced you into installing Code's Combat Alerts addon, which tells you when to dodge roll. The obvious replacement, at that point, is Order's Wrath or, if you are a templar or arcanist, Deadly Strike. You don't need the safety net anymore. That said, I still use Hexos Ward on certain builds, in certain fights, for example to solo some DLC world bosses.

If you're an arcanist, the choice is pretty cut and dry. Velothi-Ur, Deadly Strike, 1x Slimecraw, Maelstrom fire staff back bar, and X, where X is ideally a trial set, but could be something like Pillar of Nirn. The latter is a meta option in general.

I've never been a fan of Briarheart. It gets recommended, I think, because it's easy to obtain. It has been used in trials in the past, because it temporarily gives you more damage than Hunding's Rage, but ony for short trash pulls. I guess that's similar to overland, but if you want to burn a boss quickly in, say, Maelstrom Arena or Infinite Archive, you're more likely looking at Mechanical Acuity. Briarheart has the heal, but I find that heal insignificant compared to, for example, the Hexos shield or wearing Pale Order.

If you are an Oakensoul nightblade, then Stygian is something you might check out. A line of pen up to 9K, without Major / Minor Breach, is something that should beat a line of crit when you're playing solo. On a Khajiit, I'm not sure, but in general. Note I'm saying Oakensoul, because Stygian needs to be double-barred. You lose the bonus on bar swap with this set.

If you don't have enough sustain, then Vicious Ophidian is a go to set, albeit it's a trial set that, I'm guessing, you don't have. Back-barring Wretched Vitality is another option. Front bar a damage set, such as Order's Wrath, in that case. Use Pale Order as the mythic. Add a monster set, such as Iceheart, if you have that, and 1x Trainee.

The single meta crit set for your purposes is, unfortunately, another trial set: Sul-Xan. It's a meta set for Infinite Archive and any other place where you frequently have adds.

Arguably, though, you should be aiming to have fun, because everything is so easy you don't need any of the above. Sithis' Touch is a fun set that can make you insanely fast. On the other hand, if I want to quest and don't want to be hassled, my DK turns vamp stage 2 and wears Darloc Brae, 3 pieces of Night Terror, and Wild Hunt. Darloc Brae + vamp + Wild Hunt allows you to be fast in crouch while maintaining your stamina. You can add Race Against Time, and you will have the sustain for that too. A Darloc Brae back bar would also grant you perma-cloak sustain on a medium armor stamblade.

At the other end of the specttrum you can aim to solo harder stuff. Some world bosses are hard enough that you might want to be tanky. Hexos + Briarheart may or may not cut it for all of them, at least if you haven't internalised the mechanics of the fight yet. It also depends on class. Among the stamina classes, I find sorc and Crit Surge the most OP for soloing. I run my sorc as a Brawler build for that purpose. For that, however, you want a Master's 2H weapon from Dragonstar Arena. Builds that use Brawler as a spammable are slow going when there are no adds, and they are very stamina hungry. Vicious Ophidian is recommended and you may even pair that with a Wretched Vitality back bar. This, then, will allow you to solo some very hard stuff in easy mode. The combination of the Brawler Shield and Crit Surge is OP for making you tanky while killing, beating every other self-healing playstyle by a mile when you have the sustain to spam Brawler without too many Dark Deals. Sorc's damage passives are also the best for this kind of build. There is a marked difference to running this on a DK, for example. Sorc deals noticeably more damage.

The only place where a Brawler build, while viable, is lacklustre defensively is Infinite Archive as it ramps up. It doesn't get you particularly further than other builds. Infinite Archive has it's own meta.

Another mention goes to Telvanni Efficiency. If you're playing with a companion, that should be your go to set to experiment with. Paired with some Quickened gear you can create companions that are far more useful and durable than they usually are. Not meta useful, but better.

Talking about companions, the opposite way they can help you is to let them die, while you wear Pearlescent Ward. This will give you 33% damage reduction. Another trial set.

Finally, you can get past some mechanics, that may have stopped you, by using Precognition, the Psijic ult. I double bar this on my Brawlersorc and make a virtue out of sorc passives and the fact that I don't really have an ultimate to use, by speccing into health regen with Strategic Reserve CP and gold food. You can solo Cradle of Shadows and Fang Lair that way, for example. Note for Fang Lair, using a tank companion is pretty much mandatory, since you still tend to be CCd and one shot otherwise:

https://www.youtube.com/watch?v=hmdFvTrlaxQ

The best Mythic for Khajiit is almost always Mora's Whispers, imo.
With Slimecraw, Tzogvin and Order's Wrath, I can get to crit damage cap, have mid 60ies crit chance and reasonable other stats, depending on the class. This is in almost every context the best SOLO setup for Khajiiti.

Another cool combination is Heartland Conqueror and Torugs Pact. 800 WD from the backbar glyph plus a weakening glyph on steroids on the frontbar for serious protection is a somewhat balanced approach to SOLOing. If you have sources for minor and major Cowardice, you can survive any Boss fight with decent rotations.

All in all SOLOing means you need to use the right skills and have a good rotation, that allows for combat actions, without dropping too much in damage.
For example, I have a Templar build with Hexos' Ward, Prayer Shawl and Iceheart, that can reach between 35k and 40k, but have all shields up at 65% to 100% of the time. It's really difficult to die on that build.