Tuning out the longitudinal mode in the D4

I've always wondered why, when increasing the string length to its maximum, the lower bass region sounds equal parts sonorous and annoying. After viewing this link, I may have found out why. Even at maximum string length, the L-mode interferes with the perfect consonace between octaves in a significant way. So, with just a trial version of Pianoteq, I tried altering the cutoff frequency and the Q-factor, however, when the offending partials are reduced to a point of tolerability, the decay in the lower region becomes way too damped, even at maximum impedance. Have any of you tried filtering out the partials related to the L-mode? I would like to hear your thoughts on this.