Best way to hook up REL sub with single RCA input to preamp/amp combo?

One way I like to connect my speakers is as follows:

Tube preamp (Quicksilver) --> Integrated amp (Atoll INT200, using the "bypass" on the amp so I just use the amp portion only).

The effect is nice -- a hybrid setup. Solid state power with tube preamp qualities.

However, I also want to connect my single REL sub using an RCA interconnect. (I have the high level wires hooked up to my QS tube amp and don’t want to disconnect them. Too inconvenient.)

The question becomes, How do I hook up my REL sub's single, line-level RCA input to the other gear?

I tried two ways:

1. QS preamp --> REL. My QS preamp was specially set up to have two preamp outputs. In this setup, one preamp out goes to the Integrated amp section.

Y-splitter method. Problem. But when I sent the second preamp output of the QS to the sub and used a Y-splitter, the soundstage collapsed.

Single RCA method. Better but not stereo signal. I sent the second preamp output of the QS to the sub WITHOUT the Y-splitter, it was ok (but now I’m only sending either Left or Right to the sub. Seems less than optimal.)

2. The second way to connect the REL sub was to the pre-out on the Integrated. That seemed to work ok.

So, if I’ve described this adequately, how would you hook my single REL sub? To the tube pre-amp? To the solid state integrated?

Please don’t suggest a second sub. I’m already looking into that!
Whatever way uses the shortest cheapest wires. If the REL has high level inputs use those. Or use the one RCA. Remember when it comes to subs there is no L, there is no R, there is only mono not stereo no matter how many wires you use or how they're connected.
@millercarbon -- I know you're an expert on subs so I'm glad to hear that there is no right or left channel for subs. I thought that there was sub information for left and right channel. 

This is huge news for me, because at the moment, I'm running one high level wire to my left mono block and another one to my right mono bock (and the black ground to the right one, too.) You're saying "no need"? Because if that's true, I can now move the mono blocks further apart from one another. (They're close together now so I can make the wires reach to both sets of binding posts.)

So, let me ask you one further thing -- if you were running a tube preamp to a solid state integrated amp via the bypass (on the integrated) would you run a wire from the tube preamp to the sub or from the integrated to the sub?

Thank you.
I found some good answers here from Almarg (RIP) and Johnny.

Sorry to start a new thread on this topic; the truth was out there.

But now, if MC is correct, I can initiate a separation of my too closely positioned mono blocks.
Whether you get mono or stereo depends on the sub and what you have the crossover set to. 
Thanks, djones. The sub has a single RCA input and there is no crossover control on any of the amps.

In an ideal world, I'd have two subs:

Left channel of integrated (or left mono block) would go to left sub.
Right channel of integrated (or right mono block) would go to right sub.

But I have one sub, with one input. So the question is how to get a stereo signal into that sub.

But as MC has put it, there's no need because there is really only a single channel for subs. 
What I meant was what the crossover was set to on the subwoofer. If you connect only the left or right out you are getting either the left or right stereo channel. If your crossover is set for sub bass it doesn't matter since that's mono. Some subwoofers not sure about Rel you can roll off the crossover as high as 250hz so you might want stereo in those cases using small bookshelf speakers. 
@djones I see. The crossover is usually set pretty low -- it's a dial. I never set it higher because then it doesn't match very well with my speakers.