What effect will sloshing of the fuel will have upon the CG of the whole aircraft? It should be fairly straightforward to calculate since you already know the CG movement of the fuel.
Had you considered the effect on handling of a rapid stall entry, followed by pitch down on recovery? (FAR/JAR 23&25 would normally use a 3 - 5 kn deceration rate - para 203 I think, which in some types can produce a marked pitch down.) I suspect that LSS will vary through the manoeuvre as the CG moves back during the stall entry (causing a low stall speed, high elevator power, and thus steep nose-up stalling attitude), followed by a more FWD CG during the pull up, causing reduced elevator power when you actually need it.
I suspect that you'll probably find that the SPO is more damped than usual - there's a device called a bifilar damper which uses mercury in a tube that tends to oscillate in antiphase with the motion; I suspect that your tank might well do the same.
Interesting question, I look forward to seeing what wiser heads have to offer.
G