I do not think that it is a fair statement that as a class, mood stabilizers have fewer/milder side effects than antipsychotics. The only mood stabilizer with a relatively benign side effects profile is Lamotrigine and it will not do a thing for psychosis. All the others have very serious side effects. A better comparison is to see on an individual basis what each drug (not each class of drugs) produces in you and go from there.

MrAbbott, it is possible for many people to treat bipolar with antipsychotics alone. For some people it may mean taking two antipsychotics. For some it may mean just one, called monotherapy. In terms of FDA approval in the US, Zyprexa is FDA approved as a monotherapy for bipolar and is extremely effective but has a horrible metabolic syndrome side effect. Then there are antipsychotics that are not (yet) FDA approved as bipolar monotherapy but are used as such off label (outside of the official approval). From a Medline (PubMed) search:

Olanzapine, risperidone and quetiapine have been shown to be effective for manic episodes both as monotherapy and in combination with other agents such as lithium and divalproex. Divalproex is valproic acid. Since Invega is a newer cousin of Risperidone, I am pretty sure it can be effective as a monotherapy but you need to give it a try to figure out if this is true.
for you.

I could not tolerate valproic acid because of hand tremor and falling platelets. I also gained a whole lot of weight on it. I will not go back on it. I am stable on antipsychotic Latuda with a small dose of antipsychotic Seroquel taken strictly for sleep. I am not taking mood stabilizers or antidepressants. Antipsychotics fully fix it for me.

Your doctor might be going at it strictly by the book, believing that antipsychotics have to be prescribed only in combo with lithium or valproic acid or both. I especially think so because you implied that your doctor is very traditional and has a bias in favor of lithium. I think you should tell him straight up that you want to find a solution where you are on an antipsychotic monotherapy. Use this term: monotherapy. Tell him that you prefer to avoid lithium and valproic acid altogether.

How is your bloodwork? Both lithium and valproic acid therapy have to be accompanied by regular blood tests.