Subwoofer speaker outputs to increase efficiency


I own a low-power SET integrated. My speakers are rated 87db. The amp doesn't have enough juice to power the speakers well, but I hate to give them up. I'm trying to think of how I can get more efficiency out of them.

I've been thinking about getting a subwoofer (for example, the Omega sub) and connecting it via the speaker inputs. Then run the main speakers from the sub's speaker outputs. 

But I'm not sure that this is a good idea. It seems like this would degrade the sound quality coming from the main speakers, as much as it would help them to play stronger. 

Does anyone have an opinion on this? Also, would it be necessary to use the same type of speaker cable between the amp and sub as the sub and speakers? I've read that cable quality is not a big concern to a sub. But if the signal is then getting passed on to the mains, then it seems like it would be pretty important. 
rfprice
Cost-wise, I don't think you will save much by adding a sub vs. getting a more powerful amp.
That being said, perhaps a Vandersteen 2w/q sub with crossover will help? By employing a high pass filter, you relieve the amp from having tto reproduce power draining low frequencies.
B
gdnrbob +1    When I auditioned a more powerful amp with my 89db speakers, the dynamics and PRaT improved significantly.   It was most evident in the mid-bass region - by the kick in the kickdrum. I bought the amp.  The less powerful tube amp is in storage for a future 2nd system with more efficient speakers.
Yep. You're telling me the truth that I don't want to face. I need to change either the amp or the speakers. I don't want to get away from 300b, but I'm also sad to sell my favorite speakers or relegate them to the closet. The best solution is Cary's 211 monoblocks, but I can't foresee when I'll have $22,000 to spare. A subwoofer is just going to introduce a new set of challenges. 
I can relate to looking for a creative solution in order to have it all and then realizing it was too left field.
@rfprice

Now we know your integrated is a 300b set, what is the speaker?
Is it bi-ampable?
The integrated has pre-out?

The amp is the Cary 300b. It has no pre-out. The speakers are Opera monitors from 2006. They have dual posts, so I guess you could bi-amp each one. 
Try and find a pre owned zero feedback Ayre AX7 integrated
I think you will be surprised at how much of the sound you are looking for comes from the Zero feedback design itself.
 You may even discover some advantages with it and the Choices it allows with quality or performance & speakers you can now drive.
 Best,
 JohnnyR 
This thread might be of interest.  The OP also has a 300b. https://forum.audiogon.com/discussions/coherent-speakers-from-canada
Well, what a coincidence. The fellow on the thread who raves about the sound with 300b is also using the Cary and also using the exact same tube complement as I am. 
How did you end up in this situation? I considered a 7 watt SET but thought my room too big. Seems like SET is a midrange dream. My current amp has a SET output option. But I stick with Pentode. Thats me though. Your tastes may be towards the midrange magic of SET. Seems like yer going to have to make a decision. Amp, or speaker.....unless you can Bi-amp. Get a separate amp to push the other side. Not sure if that is feasible though.  We audiophools are really a different  bunch aren't we? Most people are satisfied listening to streaming music. We want it all!!. I wish you well in your search.