However, the S7 has a very flat 4 ohm impedance curve. You probably still have a lot of room for improvement. A good friend of mine has S7s. I am working with him to get the best out of them. I think you should try KT88's and I would match them even though your amp does not require this. All 8 should match! Small differences in amplitude response will affect imaging. Another approach, the one I take is to measure the system by channel at the listening position, but I have the ability to correct any amplitude problem, you do not. The amount of power your amp makes is totally dependant on the power supply. With KT88s in mono configuration your amps put out 200 watts which with subwoofers is more than enough to do the job.
The swarm is a great system for bookshelf speakers. It is nowhere near powerful enough for for the S7's. You need at least four 12" drivers. Two Magico S subs or two Martin Logan BF 212s would do the job. My friend has four 13" JL Audio subs which I am not crazy about because of reliability issues. I believe the S sub has a complete crossover in it. The BF 212 only has a low pass filter like your swarm. This is not satisfactory particularly with your amps. You need a complete two way crossover with complete bass management. I would put the subs outside the S7s in corners. This only works if you can correct time and phase. I would cross at 80 Hz. What are your program sources?
Done correctly, your system will be able to play Vini Vici at 100 dB and blur your vision or the Melos String Quartet at 85 dB and make you cry.