It is *likely* that the alt is performing fine. High output alternators will not flow at full current with the engine idle - peak output is at about 2~3k RPM typically. Check your ground after zeroing your meter:
Touch or clip the leads together after powering it on and setting for the 20 ohm range. If digital, press the "REF" button with the leads touching after the numbers settle. This makes the meter ignore it's own reistance. (They sorta "float" around .02~.03 ohms and this makes it read 0.) If you have an analogue meter, same thing, turn it on - clip the leads together after setting next to lowest ohm range, fiddle with the zero adjust knob until zeroed.
Disconnect the negative terminal off the battery and measure resistance from the negative terminal on the amp to the negative lead that normally is bolted to the battery. If it reads higher than 1.5 Ohms, you need to work on getting it as close to zero as possible. It will never be perfectly zero, but over 2 ohms is a clear and dangerous sign that you have a ground issue still.
With the battery still disconnected, check resistance between the alternator output post and the battery positive terminal, that too should read nearly zero, typically a few hundredths (0.0xx) Ohms or so should be the measurement in a good power setup.
Bolt it all back together once you are satisfied and power up the system. Raise your engine RPM up to 1500~2000, monitor voltages. At speed, your alternator should put out a flat 14.4~14.8 volts with lights on, defroster running, audio pumping. If it is still dipping with a heavy bass hit - check your accessory belt(s) - see below. At idle, even with a high performance alternator, voltage drops will be present with a heavy vehicle electrical load, but should not fall below 13 volts.
Shut the engine down after turning off everything, no interior lights going, etc. Plate saturation in the battery will make it drop in voltage at a decent clip, but a fully charged lead-acid cell settles at 12.5v after a few minutes. Any lower, the battery and/or alternator is suspect. Either can be tested for free for the asking at many automotive parts stores. Be warned though, to test it, it has to be taken out of the vehicle.
Also consider too that belt wear will make an alternator under load slip if it's near the end of it's wear limit. Fresh, tight belts are mandatory for audio setups, so keep that in mind. (I chew through one every 12K miles on my truck even with a sedate 190 Watt X4 amp and MRP-M500 monoblock)
If after the "cheap -n- dirty" checks here do not work, may have to consider the fact that your amp may be to blame after checking your sub on a donor amp or buddy's rig. Usually a bad subwoofer will make horrendous rattling and buzzing noises or not work at all if it's gone by the wayside. Also try swapping out your amp with another of it's kind or of similar design. (I know, a lot of work but it beats shelling out bucks for a new one or a rebuild)
You sound pretty sharp and now armed with a little knowledge, go forth and kick butt! I really hope that you just discover a high resistance in a line and get it exorcised quickly. Good luck. :D
Life is too short to build slow computers or weak audio!