Help finding a subwoofer

See ieLogical SubterraneanHomesickBlues

You should use line level input, roll the bottom from the mains. This will increase level available from the mains and make integration easier.

Martin Logan Dynamo also have Anthem Room Correction with optional mic.

Many subs == even, NOT Accurate, low end. Two subs near the mains provide the most convincing soundstage

'Full Range' speakers seldom are. My current speakers are 25Hz ±4dB in a typical room. Main woofer amps are 200w monoblock.

Adding a 40Hz first order Butterworth effectively doubles the woofer 'music' power and transient response is much better. Room & sub integration is much easier.

Pop music doesn't benefit much, but massive orchestra or pipe organ is a quantum leap better.

I believe in not altering (DSP etc) the signal. It adds distortion.

No it doesn't. CD digital output into a DSP offers the ability to exactly tailor the XO frequency and slope to match the drivers, something that is extremely difficult with passive XO. Additional benefits are minimum phase, time alignment, room correction and precise driver control as damping factor is preserved at Fxo instead of being ZERO with a passive XO.

99% have never heard a correctly timed, phased and crossed-over multi-amp system. Shock and awe are the usual reactions when they do. Poorly recorded multi-mic compressed one dimensional recordings are exposed as the dreck they are. Comments like "That's one of my favorite recordings and it sounds so lifeless compared to ..." 

do you mind to elaborate on what you meant when you wrote preserving the damping factor at crossover frequency

When using active crossovers - which entails removing the passive in a multiway speaker - the amplifier is connected directly to the driver, so the damping factor of the amplifier is unaffected.

An idealized passive crossover has an infinite impedance at the crossover frequency. Hence zero amplifier damping. In the real world, the impedance is not quite infinite, but can be several multiples of the nominal impedance and thus driving the damping to zero. Look at speaker impedance graphs on Stereophile and you will see impedance peaks of 10x nominal. The phase response is horrible in the XO region.

Thinking of budget I would forego xo to the Mains. And thinking about the high level input the question arise if the the worse tube amp bass performance relative to solid state is due to interaction with speakers is it then less worse going into the subwoofer. If tubes mean bad bass then I would also have to forego high level input .

XO to the mains is trivial. A simple series capacitor correctly sized to the main amp impedance. Anyone can build one in an afternoon. XO frequency should be at least ½ octave above anechoic corner frequency.

See Simple HQ Passive XO

High level sub inputs are about the dumbest idea extant. People spend silly money on fancy speaker cables and then gum up the works with a "Y-cord"

 how the input of a subwoofer is able to deal with signals from all amps in a high level input

The sub high level input is high impedance, so only uses voltage and very little current from the power amp. Level control adjusts.

A hundred-fold increase in power is only a tenfold increase in voltage and easily handled with a high resistance input potentiometer. How inaudible the additional wire and circuitry is depends on the power amp, cables and listener.

Today I threw out a Storm iii and a Stadium iii.

If the drivers are still good AND you can retrieve, you can remove the amps, fabricate a filler [or just add external connectors] you can use a 2ch class D* and DSP to blow the doors off the REL amplification.

Ported speakers are sub-optimal in many areas: phase coherence, impedance, port huffing... I'm not sure I ever heard a pair I liked.

[* I have a 150W NuPrime ST-10 listed on US Audio Mart that I used for woofer amp in my triamped mains. Other amp options abound.]