Id' like to jump in on this.. I've experienced this both with my EJ205 and EJ207 engines. I have changed, batteries optima red top/yellow top (yes it did improve but eventually came back after a few months), I've changed positive battery cable, BRAND NEW (not remanufactured) starter, all fuses were checked along with positive & negative battery terminals were changed.
The only thing that I did was have the alarm shop that I had install my alarm swap a module (I think the brain) and it started working again. Unfortunately, I'm still experincing this problem. I too have a bugeye but it doesn't just affect bugeyes. My friends 05 STI had this problem until he removed his viper alarm. I have a similar one (1/4 mile vs his 1 mile) from clifford. I'm going to be replacing my alarm soon since that's the only thing that hasn't changed. I also haven't swapped clutch sensors yet but since it's clicking I don't think that'll do it. Now after my friend removed his alarm he can start his car flawlessly with no problems for about 6 months... far beyond the things that I've changed that only lasting 3 months or so.
I haven't checked or changed my negative terminal since it isn't corroded at.
I have gotta the P0335 code but very rarely but it does come up. It hasn't showed up in a while but my ECU still had it stored.