1176 Rev A, fastest attack AND release on vocals?

Try de-essing before sending out to the comp and then again after post-comp EQ.

Or: maybe back it off to 6 on attack and see if it's controlled but not so dark? I rarely encounter a 76 set to max attack on vocals, at least in my limited circle of experience.

Tips:
Don't rely on one compressor if you want that pinned vocal sound (my favorite, ever since I heard my first Hugh Padgem mix!)
Use a V-Comp (a variety mu comp from audioscape and Retro makes a similar one) or a CL1b or an LA2a/Opto and a 76 Rev a. Ht them both HARD.
The small amounts of distortion in each will take care of shaving the transients and give you a quicker attack without it sounding like a bucking bronco or an asthmatic (like me) without a puffer after a 10 mile marathon. i.e. pumping and breathing
Mic goes into preamp. Average RMS output from the preamp should be -18 up to -12 dbFs. (or 0dBu up to +6)
input on your mu or opto should be high. on about 12 o'clock. Output at about noon also. Compress mode.
I wrote a user guide for these which goes with the Audioscape product guide.
The 76 blues tripe Rev a? The beauty is that it's like crystal shattering sound in the attack of a dialed up AC30. Sparkle and shine and is shatters the transients into magical pixie dust. Try setting the input at about 30 up to 27 and the output at 12 (numbers, not clock positions) attack 3 release 5-6. Ratio 12:1. Ignore the meters once they're set.

It's really that simple.

I tend to go with multiple stages of compression
1176 - EQ - Opto - and then MV2 in the box
I try to stay under 10dB of reduction on the 1176 and about 4-5dB on the opto LA2A. In the box, I like MV2 (Waves) to bring up the low stuff. I don't light the downward compression of it at all.
The combination works well for me but some deessing or manual adjustments of the Es's is going to be necessary. I don't think there's any way to get super in your face vocals without taming es's.

OP, high shelves bringing out sibilants is the reason the MCDSP dialog processor exists. Limit it more! But honestly you're overcompressing the signal and the 1176 is smashing down microtransients in the highs. Back off on it and use an additional compressor or two or use a better compressor in the first place to avoid overmodulating the signal by stacking 3-4 compressors in a row.

Honestly, now is the time to ditch the "classics" and learn to use the new stuff
Use one of those compressors that has a cleaner box tone or ones that use any number of a variety of techniques to keep the high end alive

High frequency expansion linked to the compression: Drawmer DL251, U-he Presswerk, Tokyo Dawn Nova GE. Discontinued stuff: Aphex Expressor.
Lower ratio in highs: Tokyo Dawn Kotelnikov GE with frequency dependent ratio, multiband compressors with first order crossovers. I like PSP OldtimerMB
Or just use something cleaner or low passed sidechain or total multiband bullshit for bullshit "modern" genres

Thank you all. I made it work by using two compressors in series, the Daking Comp II with slow attack / fast release -- about 7 dB gain reduction, followed by the 1176 Rev A at attack around 3 and fastest release, pinned at over 20 dB gain reduction. Somehow that reduced the sibilance significantly. I didn't have an LA2A available to try Ward-io-Scape's approach.

Oops . . . a link would help. The higher quality version of it really exemplifies the heavier compression

I don't as of yet, but hope to find out. I'm hearing some VCA action in there, I think . . . or ABI mode FET stuff.