If you wish to contribute more via melee, even if your melee isn't too high, debuffers are great.
Use Shattermantle against drow and devils, to lower their obnoxious Spell Resistance (especially drow).
Use Destruction and Improved Destruction to lower a mob's AC. Rahl's Might staves from Mindsunder are probably the best Improved Destruction weapons as they have good damage, decent side effects, and everyone is proficient. Just keep Divine Power and Divine Favour up, along with Prayer (+1 to damage to everyone in the party) and Recitation (+2 to hit for those without luck items).
Use a Cursespewing weapon to lower a mob's saves and damage on high HP targets like Sobrien (Claw).
Dreamspitter or Staff of the Shadow, while far less useful in epics than they used to be, are still nice to swing to occasionally land a level drain.
As for casting, it's not easy to get a reliable enough Necro and Enchantment DC, but you can occasionally kill off a caster or two even with minimal gear and a high wisdom FvS build. You just may need to use an energy drain first. For enchantments, you just need to select your targets. Greater Command does work on giants (Claw), trolls (VoN1), and a few other stupid mobs.
Bauble is very nice to have, I won't deny that. You should be trying to get it.
The Amara's and Tokala's Belt clickies are also almost essential. You should definitely get those. They make healing while swinging a weapon much better.
The Abbot loot crazy mentioned is all nice to have, but in no way essential. None of the "Efficient Metamagic" clickies are essential, nice but not essential. The staff is the best of the items, but don't hold off doing epics for 2-6 months running multiple Abbot 20th completions just for a chance to get it. The Necro and Enchantment DC bonuses can be substituted with other items, only the 'Power Store' ability can't really be replaced. And, you will only need the SP savings on the toughest, most shrine light epics anyway.
Abbot also is more "twitchy" and has much more micromanagement and frustration to heal than almost any of the "easy" epics, and also has a higher PUG failure rate than the "easy" epics. Healing Abbot is good training, but having a full set of equipment from those pathetically bad rates is not something I would expect. I personally am nearing 40 Abbots, and all I have to show for it is a single Vile Blasphemy (which I didn't even pull, I traded a WIS tome I pulled for it in chest), and a +3 STR tome from my 20th since NOTHING useful appeared on my list (no staff, blasphemy, embers, litany).
Eardweller is good to have, but still something that most of the time you won't use too often. It's mainly for stacking Divine Punishment on a low risk boss, one you won't have to heavily heal for and can afford to spend the SP on damage.
SP item, for Greensteel, yes, work on it. I personally value the HP item more on someone without evasion. That means, of course, that you need to complete 20 Shrouds to get a cleansing stone before you can make and use a second item. A first character will need to run 15-20 Shrouds just to get enough larges to make their first tier 3 Greensteel anyway, so you can't expect massively geared people for the easiest epics.
The OP has far more HP than the average PUG "healer", and more than the average PUG rogue, monk, or ranger. He has enough HP to survive rolling a 1 on Malicia (Big Top) or a Kobold Shaman's (VoN1) Disintegrate, which is far more than you can expect with the average PUG member.
And, going by crazy's SP requirements, any Cleric is pretty much excluded. Even counting an RS Cleric's bursts and aura, that won't make up for enough SP to meet his requirements. Also, don't forget that the capstone heal on any Sovereign Host FvS is a significant amount of healing between fights or in tanking situations between Heal scrolls, especially powered up with metamagics. If the average well build 17/3 Clonk can make do with 1500-1600 SP, without resorting to potions, a full FvS with 2300-2400 SP is more than sufficient even without excellent gear.
I personally am more picky about the groups I heal in Amrath than I am in the House P/D/Fens flagging quests. I will often join just any group for P/D/Fens flagging except for Small Problem and Spies in the House, as I know that if one member is sorely underprepared, the group can still succeed without drinking potions. And, that member will be taught what is needed, and will see why. Education is good, elitism is not.