The difficulty spike: how would you address this situation?

Those are definitely some points to consider, but I'll start off by saying that in the worst case scenario, the player can avoid softlocks by just simply dodging every soldier, because it is possible unless you messed with that for some reason. Naturally, that's a terrible fallback, but it is a fallback nonetheless. In response to your three ideas:

1. Personally, I find RPGs are better when the difficulty is beyond simply high stats. Ideally, if high stats are present, they can be overcome by hard counters(such as, say, Image, as a relevant example). If you've given no options this early because, well, it is early in the game, then stats that are too high to overcome are obnoxious. If it's not in the cards to add things that would hard counter physicals(such as a couple sparse pieces of good armor that heavily reduce the damage dealt to a single character when stacked, a Rage that uses Image/Vanish, a Mirage Vest type thing for Locke), then reducing enemy stats is something definitely worth considering. RPGs like Dragon Quest 1 show their age in part because enemies scale in difficulty simply by doing "damage, but more" with not too much to reduce it, and this should be avoided. It's hard to offer more specific advice without a detailed look at everything the player must have access to(mandatory/obvious pickups), as well as what the player can have access to(secrets, optional things in shops, etc.)

2. Buffing Edgar in particular is an option I instinctively shy away from. It will have a butterfly effect down the road, and may potentially make him overpowered later. It's not something you can change in a vacuum as easily as the enemies here, which only appear here(I assume). It also runs the risk of making "an intended solution" in that if Edgar is buffed explicitly to counter these enemies, it becomes necessary to use him in a certain way if the buffs must be extreme to allow him to contribute. If Edgar ends up being the weak link in many other areas of the game(especially areas he's mandatory for, such as early WoR), then this becomes a more defensible option as it will adjust his viability more naturally instead of just disproportionately making him useful for one specific area/task.

3. This runs a similar risk to 2. in that if Mog becomes necessary to add to make the segment viable, he becomes necessary to use and thus the number of viable options to beat the segment becomes smaller. I understand that he's basically just an extra character and not a solution to the puzzle in this case, but if his strengths happen to be "just perfect" for the segment, it makes him disproportionately likely to be used and this is probably a downside.

With that in mind, I'll propose an option 4:

4. Add some tools in other chests that allow players to deal with the more powerful physical attacks that are thrown at the player. I recognize I'm making this suggestion rather lightly without knowledge of how the rest of the game is balanced or what effect that will have, but one advantage you have at this point in the game is having the three scenarios. It may be that each scenario has a couple pieces of gear that make things easier, but the true value doesn't become apparent until you start to get them all. A decent example is armor. As a hilariously oversimplified example, if the average defense is 150, and each notable piece of armor grants 20 defense over the average, then the first piece of armor which changes defense from 150->170 will reduce damage by ~20%, and then the next piece which changes defense from 170->190 will decrease damage by ~25%, and the third one(190->210) would reduce by 33%. Each piece of armor does comparatively more than the last, and thus the accumulation across the scenarios would allow for better combinations when the parties finally reunite(a similar argument applies to equipment increasing damage for the sake of one-shotting enemies, for example). It doesn't stop at gear either, as you could have additional ways to apply Safe, Image, Vanish, etc. instead, and these could be gathered throughout the game.

All that being said, it's definitely possible you may reject this solution straight away based on the balancing of the rest of the game, and that's fine. If there's a lack of purpose to parts of the early game, then this could be a useful cause to point them towards.

TL; DR: Options 1 and 4 are advisable in my opinion, option 2 could be done as long as it's done carefully, and option 3 is probably my least favourite option of the group.