For those with lag issues from the battle log, I made a quick fix - extract this file into www/js/ and overwrite.
It stops the game from calling the MPP_SmoothBattleLog plugin which for me fixed the issue (had to also suppress the Add_Proc_To_MPP_SmoothBattleLog plugin, which didn't itself cause lag for me but causes an error if you don't have the original plugin).
Note that this also removes some formatting etc. from the battle log, the worst consequence is that sometimes the log can swamp the screen (it only refreshes once a new character acts, so if a lot happens during a single character's turn it takes up a lot of screenspace). You also can'tlook at the battle log history. There's probably a better fix to be found by tuning the parameters of the plugin or something but it works for me so I'll leave it atthat.
If you don't like the fix, delete plugins.js and rename plugins.jsold to plugins.js to restore the original file.
Another possible fix is to go to line 34 and set Max Lines":"6" to Max Lines":"1", you only get one line at a time but it prevents most of the lag while keeping the battle log format as in the base game, and you can still view the log history. Doing some more investigation to see if I can find a better fix but I'm not really experienced with this, if someone else wants to have a look I'd be grateful.