98 Civic shakes violently at high speeds

Was it happening when the balancing was done and continued? Have you thought about rotating the front tires to the rear. I say that as a cord problem could be causing the problem. Have you had any wet conditions lately. Wheels can be balanced then dirt and water make mud that sticks on the wheel forcing it out of balance. I have seen LAZY people running the balancer that don't put a clean wheel through the balancer but proceed to balance the wheel. Then wheel becomes clean from wash or rain and it is now OUT of balance.