You're doing something very similar I'm doing, so I might be able to offer some advice. I faced similar problems and combed the forums for solutions.

First off, since I started with just a leviathan I know your pain in dealing with devilites (and for me greaver spam was an issue too). I ended up with a choice of final flourish for pure damage or snarble for its unique charge. Though I picked FF, they're mostly preference and should solve almost all your fiend issues. Solid choice there. Abuse the massive first swing arc of these blades by shielding, attacking once then shielding again. Vog cub means you're only going to be vulnerable a fraction of a second and the massive arc interupts all grievers in front of you.

The shadow blade is great against slimes. Take one if you run jelly palace a lot.

I dislike attacking Tier 3 gremlins with blades though. The thwackers get a 2 hit combo that provides impenetrable defense if there's 2-3 doing it out of sync, an insanely quick charge attack you won't see coming (danger indicator is white for some reason) and they stun. Demo's are hell to melee at all. Since they like arena's and deconstruction zones they are going to swarm you frequently. Hit and run works, but slowly. For those reasons and because guns make gremlins dodge ineffectively without ever attacking, I take a valiance (5* blaster) with me when I might face gremlins and an elemental gun when I won't like on vanaduke runs. They're strongly resistant to elemental. I recommend getting a valiance first since it's a better all-rounded gun and a good fallback weapon in emergencies. It might take 5, maybe even 10 minutes if you need to snipe menders, but if you can clear last arena rooms with 20 robots/gremlins chasing you and the rest of the team dead you just prevented a wipe. If you want an elemental gun regardless, either go alchemer (ice/shock/prisma) or polaris. All are magnificent guns I've either seen in action or used myself, except prismatech. Don't hate status, on guns they're usually more than worth it. I'd go with shock. Rule of thumb is that alchemer is more party friendly, polaris being less so but better defensively due to knockback. Using shock is only dangerous against quicksilver slimes, but that's what acheron is for.

Constructs and undead are predictable though, I'd prefer a gun for gremlins if given a choice. Divine avengers have a nice ranged charge which you can use instead too.

Concerning being perfectly all-round: I can solo anything reliably in the game except fiends since I rely on my shield a lot. Owlite's most glaring weakness is shadow defense, which means you might need to get 2 shields.

Take either elemental option and go do firestorm citadel with some vog cub and a grey owlite. Since it's good crowns and tokens once you start beating vanaduke you can start making a crest of almire, probably the best fiend shield in the game. I'm doing that now and it's already carrying me through T3 fiend strata at only 4*, plugging the last hole in my gear set.

Avoid fiend strata untill you have your shadow shield/pierce sword. If you do run across a level, do this: http://www.youtube.com/watch?v=vUV0xsEFfNU
He takes damage once, just because he stopped moving in a circle around the room. He's not even shield canceling before his third shot, which eliminates reload time and means infinite 2-shot spam.