Should I be doing more Daily's, or is Raiding really the bread & butter of Shard gathering? I know I can also buy vendor gear and Shard it (which I've done a few times), but even that is painful now that the prices have gone up. Luckily I can at least grab Chest 1 from Crota three times a week, but that doesn't help my Ascendant situation.

In terms of how much you actually get, raiding is probably your best bet. However, if you're unable to fit that in much, dailies will help - you will always definitely get SOME ascendant materials, though it's still random as to which ones.

My other suggestion is to do public events whenever possible. If you're doing patrols anyway, pull up Destiny Public Events and see if anything's going on near you.

There are also smartphone apps:

Android

iOS

I'm in a slightly different but still problematic boat with my recently-created 3rd character (a titan). I have ascendant materials, but I'm constantly out of plasteel plating. I never had this issue with my previous characters, I think the problem with the titan is that I had a bunch of armor stockpiled when I created him, so I pretty much went straight from level 20 to trying to do upgrades. Never had that in-between period where you're dismantling greens but not immediately using the materials.

This situation will not be helped by the Ruin Wings I obtained today. Aside from leveling them, I'm also going to need to level a legendary helmet (to put on when I swap out the exotic helm I had been using). Luckily, I'm only planning to use those with the Defender subclass, which I've only just started leveling and view as an optional secondary setup for now.

Should I be doing more Daily's, or is Raiding really the bread & butter of Shard gathering? I know I can also buy vendor gear and Shard it (which I've done a few times), but even that is painful now that the prices have gone up. Luckily I can at least grab Chest 1 from Crota three times a week, but that doesn't help my Ascendant situation.

Any advice?

Definitely do Vault of Glass if you need ascendant shards. Do Crota if you need radiant shards. Break down any legendary armor you don't want or aren't going to use. Don't waste your marks just to shard gear. You can get the equivalent of 4-5 armor pieces in shards alone by raiding, PLUS any armor you might acquire can be broken down.

Do hard mode, since you get double drops without doing normal first. You will often get 6 at one checkpoint. 10-12 per raid is pretty normal if you get all the chests. I've been running Vault of Glass around 2x per week since it dropped, and now I'm sitting on 401 ascendant shards.

I'm in the exact same position. Let's do a VoG run sometime soon.