Bi-Wire with two pairs of speaker cables

Bi wiring a tube amp is very effective when you have 0 - 4 - 8 - 16 ohm connections. Use the "4" as "common" and the "0" for woofer, and the "16" for the tweeter. Polarity of the tweeter may have to be reversed. Easy enough.
Now the thinner (usually) 16 ohm wire inside the transformer only carries the tweeter current. Thinner wire has better skin effect properties for higher frequencies too.
The voltage on 0-4 and 4-16 pairs are the same but phase is opposite with 4 as neutral. 8 has lower voltage, which can be OK is the tweeter is "hot" and you want to lower it.
Try it. Nothing bad will happen.

I’m a big proponent of biwiring.  I use homemade silver braid on my lows, limber monocle for my highs and I love it. Cleaner tighter bass, colorful mids, crystalline highs!

FYI: I've used the method with good success that williewonka suggested above. Give it a try...

@thyname

I do not dual wire my speakers ...I tri-wire them, and like others who have posted I use identical cables when tri-wiring. No problems here. My speakers are vintage from the early 1970s - a pair of Pioneer CS-A700's - but the cable is new. Pure copper cable. USA Made. Make certain you label your cable runs. I suggest labels at both ends and in the middle. To my ears tri-wiring is wonderful.
But then, my ears are vintage - just like my rig.
Happy listening.

Thanks everyone for your input!

I decided to order a single run of Crystal Clear Audio Magnum Opus speaker cables, plus the matching jumpers.

http://crystalclearaudio.com/products/magnum-opus/

I will do the trick @williewonka suggested (Red speaker cable to HF speaker binding post, Black speaker cable to LF binding post).

When / If budget allows in the future, I will get s second speaker cable pair, and bi-wire then