Technically I agree on the possibility of hooking up your sub via the tape loops and the headphone out. They will work guaranteed.
However, how will you resolve the crossover since your preamp does not have a low-pass filter for your sub.
This is already being done for so long by stereophiles, for 2.1 long before HT came into the picture. An external active electronic crossover circuit is used to sit after the tape out and before another amp, integrated or power feeding a passive subwoofer. The active crossover of the powered sub does the same job. It does the job of actively low-passing the bass and blocking the rest. You only need one such device when filtering.
But you're righjt, you have to set the sub's crossover at the -3db point of your main speakers, typically in the 40hz to 50hz range so that it augments the main speaker's low freq roll-off from that point, with less dovetailing. Some would set it even lower so as to preclude some possible overlaps if the rolloff on the sub is not steep enough. Or you can do a less elegant solution of turning down the bass control of your preamp if it has one, since the tape out signals do not pass thru the volume/tone circuits of the preamp. Your ears will have to do the balancing, or use an SPL meter.