Unless there was a very specific bug in the two instances of CE that I checked this in, energy weapons do 1 point of damage per hit whilst the Entity is in absorbtion mode. You could grind maybe 200-300 extra out of it by firing on it whilst it's absorbing. That's very rarely going to decide a position.
Not to mention extra DPS you get out of not repositioning yourself during and after absorption phases, and alpha striking with stuff like GDF right after the shockwave when you're at critical hull. That will decide position.
That said, I decided to do a few extra CE runs experimenting with ships and builds, today and last night just to see what's up. Now, I'm a science captain and haven't played long enough yet to have ground out T5 in NR/Omega, and the dilithium/zen to be kitted out in Z-store/lockbox ships with Mk XII purples, so I considered even having placed a success. I fully understand I won't be competitive with someone who has a Z-store ship, all the latest goodies, and a few hundred thousand dilithium sunk into their equipment, and I'm totally okay with that. My ships are the free prometheus, mirror universe sovereign, and mirror universe RSV; for the average level of gear (blue/purple Mk XI exchange and mission gear), they are equipped and slotted properly.
On my cruiser (6x disruptor, quantums fore and aft, by the by):
Run 1: Circled the CE nonstop spamming FaW and EPtW, ignoring and healing through shockwaves. Nada.
Run 2: Focused on keeping shards and tholian adds down, moved out of the way for shockwaves and to attack adds. Nada.
Run 3: Used heals and buffs on other players, moved out of the way for shockwaves, concentrated on CE. Nada.
On my science vessel (quantum x2 fore with technician doffs to ensure constant torp steam, beam arrays elsewhere):
Run 1: Exclusively healed and CC'ed shards and tholians. Moved out of the way of shockwaves. Nada.
Run 2: Focused damage on CE, used science boff powers on shards while healing. Avoided shockwaves. Nada.
Run 3: Same as run 2, but ignored shockwaves. That worked about as well as you'd figure in a science vessel.
Run 4: Swapped out my weapons to DBB x2 and photons fore, turrets aft, same as run 2. Still nothing.
On my escort (quantum x1, DBB x1, DHC x2 fore, all turrets aft):
Run 1: Focused on taking down adds with AE, avoided shockwave. Nothing.
Run 2: Focused on CE, avoided shockwave. Nothing.
Run 3: At this point I was a little loopy and decided to just be the biggest jackass I could during one run, to hell with results. I put on the Breen set, put dual rapid reload transphasics and dual DHC's fore, turrets aft, ignored everyone else and all adds, ignored the shockwaves, and just spammed every DPS ability I had on my bar. I blew up twice during the FA and still placed, whereas every prior attempt to actually play the event as apparently intended failed.
Either transphasics and the Breen set are just that freaking good and everyone who says they suck have absolutely no idea what they're talking about, or it's more advantageous to just game the encounter and bugger your teammates in the process.