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
Post removed 
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?