Should I use long interconnects, or long speaker cables?

Long speaker cable is best if your not running balanced as with single ended you will loose sound quality.

Its not acoustic feedback. Unless maybe you have the flimsiest turntable ever made and it has a dust cover and you leave the dust cover on- and even then I seriously doubt it. What you have is mechanical vibrations coming from the floor and rack right into the turntable. Springs under the subs helped, but it wasn't the subs. They helped by reducing the vibration energy the subs were putting into the floor, from where it travels up into the turntable. 

What you want are springs under the turntable. Its very important with springs that they be matched to the mass of the component. Generally speaking you want a spring that will be compressed at least half way under load. If your turntable compresses the springs half way or more give them a try. Also check to see how it bounces on the springs. If it bounces fast the springs are too stiff. What you want is nice and slow, 2Hz at most. 

The cheapest/easiest springs to try first are Nobsound from Amazon. With these you can remove springs to adjust for load. They come with 7 per unit and you will probably need only 3. My table is 75 lbs and I only use 4 springs each to do four corners. At under $35 including shipping these are an amazing deal and should definitely be tried. They WILL fix your problem. 

The Nobsound spring test will prove I'm right, and you will be able to use them under speakers and other components as well. Then once you know just how good this works the next step are Townshend Pods, which take spring engineering to another level. Pods use a bellows and air valve for perfect damping to allow micro vibrations to be completely absorbed while controlling larger amplitude movement. I recommend Nobsound because they are cheap and well worth trying. I recommend Townshend because if you can afford them they are much more refined and well worth the extra investment.

I am using long balanced interconnects (3M) and very short speaker cables to my mono blocks. This arrangement has proven to me to be the best in sound quality.

ozzy

+1 on Balanced interconnect/short speaker cables, @ozzy .

Rumble from a turntable is most likely due to poor isolation. Either the turntable itself, or equipment being influenced by vibrations.
Also, improperly set up subs can accentuate rumble.
It's hard to pinpoint without knowing what is in your system, how you are placing equipment, as well as how your room is set up.
You can post images in Virtual Systems. It would help alot.
Bob