Another thing to remember is that when you compress multiple times in series, the ratios become multiplied, not added:
So a comp @ 12:1 into a comp at 2:1 would have a final ratio of 24, which will limit the peaks pretty heavily.
The 1176 is great at catching peaks and adding some presence, and the 2A is great at very smooth controlled vocal compression. Try experimenting with the 1176 @ 4-12:1 taking of 2-4dB of peaks (less gain reduction for higher ratios, but it all depends on the music) and then the LA-2A in comp. mode taking off another 2-3dB on louder passages.
Compressing like this usually seems to take a small amount of high end out of the signal (depends on the comp), so try using the Pultec after to add some 10, 12, or 16kHz. You also might want to experiment with high-passing the vocal or EQing out some low end pre-compression, so that the compressors won't be reacting strongly to less important frequencies in the vocal track.
The more experience I gain, and the more I experiment, the more I am finding that in at least 75% of the cases having 2 or more processors working a little is much better than using one heavy-handed. This applies to compression/limiting, EQing, and with time-based processing. Sometimes you will only want to run the signal through one EQ or comp, going for a strong pumping/squashed or filtered effect, or in a purist recording when you want to keep the signal path as clean as possible (running through the least amount of gear)...or in the case where the material was recorded very well and only needs very little (or no) help.
Another example, regarding EQ: say you want a certain warm tone/color on the vocal that would sound great, but is not natural. Instead of using a lot of EQ adding low-mids or altering the upper-mids, use a strongly colored tube pre to add a bit of this, then pick a compressor that slightly colors the signal this way too. Now you might be able to EQ a lot less or not have to EQ at all. Sorry, by now I am kind of rambling and getting off topic. I like Guiness.