Nice analysis; as I'm soon going to be starting getting Alpha slot stuff together on my Crab, I've been wrestling with the same question. Unlike with a couple of other of my characters, theres not such an easy answer (darned VEAT versatility! 
I need to fight the build against some AVs to see if I need the End Reduction, part of what I figure my Crab contributes beyond what a blaster would do is -resist debuffing. With Venom Grenade plus Frost Breath, thats -35%, as good as a rad defender can produce, but also requires firing two AoEs off pretty frequently, which could be rough in an AV fight. While one could argue fighting AVs is a small part of the game, its also the part where teams are most likely to stall in end game (think LRSF, STF, Reischman, etc.), so IMHO thats where it actually starts getting important what your build is. Frankly, if all you were running was paper missions, you'd never need to move beyond SOs. So Cardiac may be the way to go.
On the other hand, since I see the main role of a Crab on a team to be supplying damage, ideally AoE damage, that makes an argument for Musculature. As you showed in your numbers, its roughly 10% extra damage, and if you have purples slotted you can even put the proc IO in instead of the Damage IO, still have beyond ED damage and the procs on top of it.
Spiritual is nice on the long recharge powers, and bumps survivability. If you look at the extra 56 hit points you list for Serum, and assume its roughly perma (which it should be with a good IO build plus Spiritual), 56 out of the ~1480 hit points total you have with it running is about 4%, so its about the same as the extra resist numbers you cite from the Cardiac IO except that its "resist all", so covers toxic, psi, etc. I also actually do like the Stun that comes with it, I have the purple Stun set in Omega (plus a damage in the 6th slot) because a Crab doesn't have a lot of other crowd control options, and its handy for if the tank is getting overwhelmed, you want to stall an ambush, etc. While the baddies are wandering around, I can generally AoE them to death with my regular chain. Ironically, as you noted, a Crab is one of the few ATs that has a full AoE attack chain (and then some) so doesn't get to do significantly more damage with more recharge, other than maybe a bit more from Omega and faster pet recharge.
Finally, one other note on the Nerve Radial Paragon, Omega does actually take Taunt, so there might be some benefit from taking the Radial rather than Core if you don't need the 45% Acc vs the 33%, as I suspect is the case for most mature level 50 builds.
I'm facing this dilemma myself w/my crab. I went through a similar analysis as both of you, but reached a slightly different conclusion. Then again, he's not yet 50, and won't know how he plays out, esp end-wise, at that level.
I was originally going Cardiac, cuz my crab expects to have some end issues, and I find Cardiac pretty much a game changer w/toons w/any end issues, plus the extra res, while not much, wouldn't suck either. I usually love the extra range for my cones, but I'm only planning on using Suppression; all the other AoEs are ranged.
My other usual option is Spiritual--Spiderlings are already perma, but Spiritual would make my Disrupters & Strikers (going Mu for concept) also perma. Still, a 9s & 13s downtime for those two isn't exactly bad. The extra heal for Serum (already well perma) would be nice though.
Nerve is what I settled on (or will settle on once I hit 50). Ranged & AoE def are already capped, but w/Nerve Core Paragon, my melee will come up to 40% and psi (for non-positional psi) to 37.5%, both of which I can cap, but would sacrifice some recharge, so I'll likely leave them at those level. The extra def buffs for my teammates is icing. Oh, acc too, but not really necessary w/Tactical Training, other than it lets me underslot for Acc a bit here and there.
Ultimately, any of the three are golden for my crab--musc is usually my least favorite, and by a long way. If I find my end bar manageable at 50, I'll go Nerve; if it's really a pain to keep up, I'll go Cardiac. W/a 4.6s downtime on Hasten already, I think I won't really miss the extra rech. Spiritual brings.
An Offensive Guide to Ice Melee
When I began alphaing, my criteria at that time was "Out of Acc, Dmg, End and Recharge, which one of those will help this character the most right now?" It recently occured to me, while looking further down the tree for my toons, I should have started at the end state and mapped a way to get there. So I'm going about the process of a more thorough analysis of what different alphas do. I'm taking a look at my Crab soldier now.
Cardiac Core Paragon
This is a Crab, so yes, Endurance isn't easy though it's managable with the build I currently have. I don't find myself chewing a blue unless there's an extended fight (say Reichsman).
This also gives Range and Resistance, both of which are desirable.
End drain from toggles goes from 1.87 to 1.41 end/sec.
I won't list them all, but end consumption on aoes decreases significantly.
Resist numbers all look better:
s/l from 50.6 to 55.5
e/n/t from 39.4 to 43
f/c from 50.4 to 54
My shortest range attack increases from 50 to 60 feet.
Cardiac Radial Paragon
Not evaluated - Fear, Sleep and Intangibility don't apply.
Musculature Core Paragon
Who doesn't like more damage?
Because there are so many attacks, I'll just look at the hardest hitting ST and AOE attacks
Longfang goes from 320.3 to 353.2
Bile Spray from 226.3 to 247.8
The immob duration from School of Sharks goes from 38 to 44 seconds. Whatev.
Def debuff from Suppression and Heavy Fires increases from 7.5 to 10.
Musculature Radial Paragon
This one is chock full of goodies.
Slightly less damage, but buffs End Mod and run speed.
Longfang is now 345
Bile is now 242
Endurance Recovery goes from 192% (3.78 end/sec) to 200% (3.93 end/sec)
Ninja Run + Sprint is my travel, so run speed goes from 63 to 68.6 mph.
Nerve Core Paragon
Accuracy, Hold, Defense
I've got TT:Leadership, 66% global Acc and a smidge of def debuff to boot, so connecting isn't a problem.
The hold is irrelevant.
I'm currently soft-capped to Range and AoE, at 42.3 Melee. Slotting this gets Melee to 46%, the others to 50. Nice. Team defense buffs (TT:M and Leadership: M) go from 20.5 to 22.7.
Nerve Radial Paragon
Not evaluated. Same as above but with additional benefits to confuse, taunt and fly, none of which I do.
Spiritual Core Paragon
Recharge, Stun and Healing, This could be interesting.
Global recharge is currently 128.8. Practically speaking my ST and AoE chains are seemless. I'll look at Omega Maneuver, Reinforcements, and Serum.
Omega recharge goes from 134.4 seconds to 115.1
Reinforcements from 302.4 to 263.7
Serum from 112 to 101.
Stun isn't something I'm looking for, even though Omega has it, so not a factor.
The heal from Serum goes from 838.4 to 950.8 +HP goes from 410.8 to 466.8.
Regen goes from 206% (20.9 hp/sec) to 219% (22.9 hp/sec)
Spiritual Radial Paragon
Recharge bonus in this goes from 45 to 33, but has other useful goodies, most of which I can use: To-Hit (for Tactics) and Jump. The Slow doesn't help.
The recharge numbers mentioned above increased.
Omega is now 119.6
Reinforcements 273
Serum 103.4
TT:L to-hit goes from 15.8 to 17.2
Conclusion
I've already gone down the Cardiac path. Spiritual Core Paragon looks like it may be a better choice, but not SO much better that I'm going to change direction.
I submit this post to see if my reasoning is flawed and if there's some consideration I missed.
Global = Hedgefund (or some derivation thereof)