Wellbutrin IS a slight stimulant. It could be the best stimulant for you when taking your schizophrenia into perspective.

If you just had psychotic episodes, I wouldn't worry much about long term treatment with stimulants (like myself) but if you were actually diagnosed with schizophrenia by a professional, psychosis doesn't go away so you're right that stimulants would be risky.

Antidepressants do increase my aggression/agitation, etc but it's only in the first few days or weeks. Eventually it subsides so you have to wait it out. Especially on MAOI's and SNRI's.

It is possible to have schizophrenia and ADHD. Maybe trying different antipsychotics will decrease the negative cognitive effect of schizophrenia because for some people, I've heard that some antipsychotics do help with the thought impairment.

I've been taking fish oil for a while and I think it helps. I've heard good ratings on that. I watched a program on TV where they were testing this guys IQ before and after taking fish oil and the longer he took it, the higher he scored on the test. Maybe it actually increased his IQ or it improved his cognition to help him score higher on the test.