Is it necessary to use the same cable brand and model for bi-wiring??

All of audio is about tone control. What difference does it make if I change speaker around to suit my cables, or change cables around to suit my speakers?
People basically change gear/cables around to suit their personal tastes. It's nothing to make a fuss about.

No, it is not "necessary" to use the same brand and model of cable for bi-wiring, just as it is not necessary to use the same brand and model of amplifiers when bi-amping.

Well it sounds like you have two dissimilar pairs of speaker cables already. So you can try the experiment on your own. I've done it, don't worry, you won't blow anything up.
See for yourself if it works or not, let your own ears decide.
Let us know what you think.

Oh, and I have used cables as tone controls. I think everybody does, some just don't like to admit it. If you choose a cable that sounds best to you, in your system, then you are choosing the cable that matches the tonal qualities that you like best. Hence, using cables as a tone control.