I use multiple tools but they main 2 are DarkEbootFixer v.3.5 and TrueAncestor EBOOT Resigner v1.4
What I do is make a few eboots with all the different methods from these 2 apps and put them all in the game via FTP but I rename them, EBOOT1, EBOOT2, EBOOT3 etc. I then rename each one at a time to EBOOT then try the game. If it works I delete all the others and keep the working one. I'm not sure which way I made the working eboot but the last time I tried 8 eboots and the 5th one worked for me. That was LBPKarting.
I was still unable to get the 1.01 update to work even after 8 or 9 eboots.
FIRST THING is RENAME the original eboot to EBOOT.BIN ORIGINAL so you have a backup.
Thanks! When you try to extract the update pkg, do you get error about the name string being to long on pkgviewer? I tried extracting the whole thing and kept getting that. I try the same tools and see what I can come up with.