"If you're going to carry around a Leviathan than there's not much reason to carry a piercing sword as well. Levi will do well enough."

Let me disagree on this, having a piercing sword is awesome against beast and fiends, due to its unique attack pattern and its huge bonus damage. On the other hand, I find that a nightblade (acheron) is not that useful if you carry a Leviathan, as Levi charge attack is much better (in my opinion), and will often do more damage due to multiple hit, even if acheron has bonus damage ... Didn't test Gran Faust yet.

I have a levi plus shivermist and have great capabilities, I take longer to clear rooms but do so with lower risk, also lowering the risk for my party members. Of course you need to learn to use the weapons for better effect, it isnt just to spam them, but once you learn the efective strategies they are great. (ie with levi you fight along the walls, so that you sidestep and charge them next to and into wall and do three hits without inconveniencing your partners... most of the time (sometimes this leaves the monster put on their only escape route, during an arena usually when you happen to run circles in opposite ways) The Levi charge is not only a tool to kill your partners you can hold the charge and wait to use it to push enemies away from them saving them :P

I've played with faust users and while the sword is good as it kills quickly I dont think it has a lot of crowd control since its charge has a high chance of screwing you up and its regular swing while wide wont push enemies as far as a levi can and wont put them to a stop like the shivermist can. I haven't tested it myself though so perhaps what I've seen isn't accurate. Assuming someone else is helping you control the mobs you can do the dps though. In that sense divine avenger would be better since its charge is better suited to kite without screwing you up.

This leaves enemies that aren't safe to get too close to. While levi is an all around weapon if you can get better weapons for these cases then do so. ie. Mass greavers (8+) You can't run away from them, so you either kill them quickly or prevent them from moving, shivermist isn't that great, its only half way there if you have the time to plant a bomb and freeze at least half of them. I'm going to assume a vortex bomb would be great vs these, a super effective sword would follow if there's any that can one or two hit them, otherwise nitronome is the only thing I can think of.

Guns for devilites and lichen colonies would be safer (again slower, but you can abuse a devilite into a corner, or do some lucky shots while backtracking relatively safely)

You definitely want any bomb to do chip damage to butterflies when you have a mob you cant get close to. A gun for enemies that dont get healed and you cant get close to but that you could use a shield against, and swords to dps single targets You original set looks fine to me since the hail driver will do gun job along some freeze and gravitron will do the rest of the job when it is necessary, when you use gravitron you'd rather use something that deals damage over time (ie. a status bomb, status gun, whatever) to take advantage of the trapping time you get with each bomb. Charging your levi can work but wont help everytime since you might not trap the full mob (last round of arena) then closing in will be too risky.

I think using the Brandish line would be a great option if you're iffy about using the DA. I use the DA mostly only for its charge which is great for keeping back crowds of Zombies in FSC while still dealing good damage. But when it's just 1-4 Zombies, I pull out my Glacius and either charge it or rush at 'em with the normal swing combo; either way it packs more of a punch than a DA. So, I guess what I'm trying to say is it all depends.

On the matter of Alchemers, I too think they're great for a secondary weapon, especially in FSC. I bring my Hail Driver with me to FSC and with the right shots, you can really obliterate those Zombies. The charge ain't too shabby for Vanaduke either... :D
On the matter of the Silversix/Argent Peacemaker, I think they're only useful in FSC; you shouldn't bring them anywhere else. They're useful for dealing damage through the barriers in FSC and also good for dealing decent damage against Vanaduke while still having decent mobility, which is vital in the throne room because you don't wanna get smashed flat as a pancake by VD, nor would you want to get impaled by the Slag Guards.

So, back to your main topic of four weapons... I would suggest:
Normal: Leviathan Blade
Piercing: Final Flourish/Barbarous Thorn Blade
Elemental: Brandish/DA Alchemer/Silversix (I wouldn't suggest getting a Argent Peacemaker because there's not much of a damage difference between a Silversix and Argent Peacemaker)
Shadow: Acheron

I hope I helped! :D

All credit goes to the people who worked on the Bombing Guide. http://wiki.spiralknights.com/Bombing_Guide

Dark Briar Barrage

Bomb Category: Damage

The Dark Briar Barrage (DBB) is a piercing damage bomb with characteristics similar to the Nitronome. It has the same movement speed while charging and radius of the Nitronome but has a slightly longer fuse[1] and has no knockback. The Dark Briar Barrage is capable of knocking down soft-bodied enemies such as gremlins and wolvers.

The absence of knockback makes the DBB a great choice for bombers less adept at nitronome placement. The non-disruptive nature of the bomb means that teammates will not have to make adjustments to their gameplay and also means that several DBBs can be comboed together effectively without interfering with each other. The DBB is an excellent choice against fiends, beasts, undead, and gremlins. Because it deals pierce damage, it is ineffective against slimes and construct.

When attacking enemies neutral to piercing (undead and gremlins) the DBB has the same damage output as a Nitronome.

Because the DBB has no knockback and a longer fuse, it offers less protection and must be used differently than a typical blast bomb. Bombers can take advantage of the DBB's longer fuse and non-disruptive behavior by running away from enemies while placing down DBBs and essentially kiting them into the blast zone. Another strategy is to take advantage of the lack of knockback by overlapping multiple bombs' blast areas on an enemy's position (like a Venn diagram[2]) while dodging attacks normally. This will allow bombers to easily hit a target multiple times without having to predict where enemies will be pushed.

Potential Hazards:

Lack of knockback will require you to avoid many attacks as if there were no bomb.