Can I have Orthodox liturgy and Latin theology?
I believe you can, in a variety of Eastern Catholic Churches.
LOL! What you actually want is Latin structure (along with the theology), because the Orthodox churches are, alas, a little dysfunctional.
Because they have rejected Rome, they’re so ethnically identified that in the US - where there are many different ethnic groups - it’s like being part of your local Cosa Nostra. They don’t talk to each other, they’re trying to kneecap their rivals, and, actually, none of them really accept Americans from outside of their ethnic group very well.
I knew the daughter of an Orthodox priest in the Midwest who told me her father kept a gun behind the altar because another priest had been shot dead by a rival Orthodox group (same Slavic ethnic group, different faction). So they need to get back to St Peter.
BXVI really wanted to reconcile them, and I think Francis does, too. So let’s pray really hard for that!