The best way to solve this issue is simply to look at the reasons why people pick or avoid AST vs the alternatives.
First, some clarification, the following views are from my own end game (Alex Savage) orientated perspective.
AST+SCH and WHM+SCH are entirely on par, WHM offers up better personal burst DPS/HPS whilst arguably being the traditional safer hand. AST brings more mobility and is a little less needy on the group overall. I consider the DPS contribution to the raid to be somewhat similar between the two. I still feel that despite the parity, AST is still considered the gimmick alternative by the community at large, but this is something I’ll address later.
So why does AST fall flat when in the 'off heal' role? It's a combination of three things: SCH brings roughly double the personal DPS whilst still being able to offer up a significant amount of sustained HPS and lastly, Indomitability is incredible right now.
So what's going on? AST and SCH have broadly comparable nukes (ED offsetting the lower potency of Broil) and SCH's dots are better but not to the tune of twofold (135+25SF vs 110). Imo the biggest factor is simply that a SCH can stay in cleric longer thanks to fairy healing and get back in to cleric faster due to being able to unload significantly more HPS within a single GCD due to Indomitability and Lustrate. End result, the SCH can simply spend significantly longer in cleric stance and has a better kit to take advantage of this time.
On the flip side of the coin, an off healing SCH also has considerably more burst aoe healing potential than a Noct Sect AST as well. This is particularly apparent in content like A8S.
So what can SE do? Here's my suggestions along with a few simple explanations behind my thinking:
First up, as mentioned at the start, I honestly don't think AST will ever shake it’s gimmick healer tag with cards as constrained by RNG as they are. So that's the first thing I'd fix with arguably the biggest change of all my suggestions.
1) Redraw's recast time reduced from 60 to 2.5 seconds but is also no longer an off GCD ability (aka it handles like Regen or Aspected Benefic).
Whoa, OOOOOPPPPP I hear you say, I totally disagree, yes it will be a substantial boost to the effectiveness of cards but at the expense of their personal HPS/DPS. Another important detail is that it'll offer an alternative means for a cleric stance shy healer to add to the group's overall DPS without actually having to 'man up' and do it themselves. And no it won't end up with 24/7 enhanced balance for all, remember that at the end of the day that AST is still only generating a card every 30 seconds and this doesn’t change that.
2) The Bole changed from 10% damage reduction on a target to 10% extra healing received on a target for 30 seconds.
Bole is pretty much Royal Road bait right now, this change makes it a much more interesting and versatile proposition whilst still keeping it a useful card during the levelling up grind with all the inevitably squishy tanks. Effectively an AST's answer to Fey Illumination.
3) The Spear changed from recast reduction to a 150 potency regen on a target for 30 seconds.
Another big change! No guts no glory right? As things are, Spear is pretty much up there with any click bait you’ll find on Facebook. it's the least desirable royal road buff and the card itself is useless in the current PvE endgame. This change takes advantage of it being a non desirable RR card by making actually rather tasty to throw out on a tank. It also opens up the option of holding onto one with spread for a bit of extra healing if needed. it’s an AST's answer to Embrace and Whispering Dawn. Naturally it'd need a more fitting name but details details.
4) Essential Dignity, Potency increase on low HP becomes a Diurnal Sect specific effect, Nocturnal Sect adds a 15 yard radius.
Quite a significant buff for Noct Sect here, giving it a non spammable instant aoe heal in line with Indomitability. Having it targetable adds flavour akin to Gravity vs Holy.
5) Lightspeed no longer reduces damage dealt by attack magic.
This always struck me as a wuss out penalty from a team that didn't grasp just how much aoe damage a SCH can do, removing this gives an off healing AST the means to compete efficiently and effectively when it comes to occasional aoe phases.
6) Celestial Opposition extends the duration of beneficial effects by 15 seconds, up from 5 seconds.
Another change to help improve overall card consistency as well as get even more mileage out of Luminiferous Aether and thus extra MP and enmity reduction to get some extra mileage out of those juicy gravity spam windows.
7) Malefic II gains the additional effect: 15% chance the next Benefic II will have no cast time with a duration of 15 seconds.
Much like the Benefic 1 proc, this will help both AST stances be a little bit gutsier with cleric stance.
8) Nocturnal Sect increases healing magic potency and all damage dealt by 5%.
A small common sense tweak. The sect buffs always struck me as backwards and this helps straighten that up a little.
And that's all folks. Personally I think this would go a long long way towards making the raid community take AST seriously as a very viable alternative alongside either healer. Whilst the card changes will mostly benefit both sects, before you scream overpowered, remember that a main healing AST is unlikely to be able to spend many GCDs on redraw and alongside a particularly DPS heavy SCH, it could even be considered a nerf (which imo is counter balanced by both the card improvements as well as the Celestial Opposition buff). However, these changes bust open the game for an off healing Noct AST giving them far more compelling gameplay options, you can spend GCDs chasing those perfect card combos. The massive gains in consistency mean you can actually plan to have specific card buffs at specific times to enhance your AST galvs, push out more aoe healing or even use your cards and cooldowns for outright HPS, a minutes worth of 225 potency single target regen (or 1:30 at 150) anyone? Just don't let the BLM know! Line up your cooldowns well and you can achieve a 33% uptime on Luminiferous Aether whilst pushing ever longer card durations. And of course this combined with lightspeed gives gravity spam an additional extra bite much like WHMs with PoM/Holy.