I find the most common alt conflict I run into is related to raiding each other. It presents a challenge, as you are faced with needing to remove your defending character or wait until they are killed or not participate in the raid at all.
It seems silly. We are all already constantly facing alt-hostilities. We all have intel that could betray our alt's factions. But, we all have learned to keep that knowledge separate. Don't warn a defending faction of an upcoming raid from your alt, don't tell one faction if the other has recently repelled a fail raid and is weakened, don't warn about the number of defending pets, etc.
Why not allow us to actively raid our alts hostile factions? I can understand the potential for XP abuse, but that can be addressed separately from the damage reduction.
My suggestion: Get rid of the auto missing that happens when an alt attacks or heals while in the presence of another alt, if the 2 alts are hostiles. Reduce the XP gained on both characters to 0 while on the same square, but allow them to fight each other.