Here's the process you would use to find out which amp is better suited for your sub:
1. The Kenwood is a two channel amp whose specs say that it will output 460 watts into a bridged 4 ohm load. It also gives specs for stereo 4 and 2 ohm operation. To figure out what a 12 ohm bridged load would be, look at the highest impedance (ohm) spec rating: 2 X 150 watts @ 4 ohms. Use Ohm's Law (double the impedance; halve the power) to find what a stereo load at 8 ohms would be: 2 X 75 watts. Note: you are using the highest load rating because your 12-ohm load is high impedance, and you want to use the specified power output of the nearest impedance to yours for your calculation.
A bridged load of 12 ohms is the same output as a stereo load at 6 ohms, the same reason as the more familiar "bridged 4 ohms is the same output as stereo 2 ohms" (notice that in the specs you posted...460 = 2 X 230?). Now, you know if you wire that sub in series for a 12 ohm load, you have the equivalent of a 2 X 6 ohm impedance. If the Kenwood amp outputs 2 X 150 watts into 4 ohms, or 2 X 75 watts into 8 ohms...the output for 2 X 6 ohms would be exactly in the middle of those two outputs because 6 is exactly in the middle of 4 and 8. The amp would output 2 X 112.5, which is 225 watts. IIRC, this sub is rated up to 300 watts nominal power. The RMS rating of the sub should be in the forefront of your decision.
2. You have the option of wiring your sub's coils in parallel for a 3 ohm impedance. The only amp of the two you have that will accept that load is the mono amp, because as a one-channel amp it is capable of taking a 2 ohm load. So, figure out how a 3 ohm load will do with the mono amp. Use RMS numbers if you have them available. You wrote, "400 watts RMS at 4 ohms, and 800 watts MAX at 2 ohms." I'm going to guess that the RMS output into 2 ohms for this amp is more like 600 watts. To find the output into 3 ohms, it's the middle of those two ratings, which should be about 500 watts. That is too much power for the sub. Into 12 ohms, it would make 150 watts...not as good as the two channel Kenwood. wildkartunes suggested the best amp for you to use.
To answer your other question: a mono amp with two sets of terminals allows flexibility in wiring multiple subs, but only one set could be used just as well. When two subs are connected using both of these terminal sets, the two are connected in parallel at the amplifier, which halves the impedance (two 4 ohms subs connected this way puts a 2 ohm load on the amp). Their wording, though, is confusing because they're referring to this method as "stereo". The warning is because of the drop in impedance if parallel connected at the amp. And normally a dual voice coil woofer is not wired as they suggested - with one coil to a set of terminals on the amp and the other coil to the other set, because it's simpler to wire the coils together on the sub itself.
Build the box so that it performs well in the worst case scenario and, in return, it will reward you at all times.