If we marry outside the USA, it might be in a third country, say Cyprus.

I return to the States, submit my I-130, and when I get NOA1 submit the I-129F.

Let's say the K3 proceeds faster than the CR-1. So, she passes her interview in Cyprus, gets the visa and comes here.

If we do the AOS here, with Advanced Parole, she may have some hassles travelling in Russia and returning to the States. (The hassles are caused by Russian authorities -- you can read about those on other threads. I've heard of other, similar problems from Russian friends of mine.)

I'm wondering if it possible to let the I-130 chug along to approval, even if she is here on the K3 that she could gain in Cyprus, do the AOS through NVC and then have her travel to Moscow for her CR1 interview. (She'll be needing periodically to travel to Russia anyway for family and business reasons.)

This variant of the process might allow sooner reunion while preserving the benefits of immediate permanent residency provided by the CR1. I think others have taken this path, but I haven't quite understood how they kept both options going along.

You read it right. Say she goes and gets the K-3 and comes to the US. The NVC still receives and starts processing on the I-130---if you respond to them and send the right fees & applications, the NVC begins the Immigrant Visa application and it eventually goes to Moscow, where she returns and has her IV (CR-1) interview.

But if you are seriously considering marriage in Cyprus, be sure to read up on filing the I-130 in Nicosia instead of the US. You might be able to both come home together with the IV afterall.

The US Embassy has already emailed me that they won't do direct consular filing since neither of us is resident in Cyprus. They would do the K3 interview if we get married in Cyprus but they say that the CR1 interview would take place in Moscow.

Who knows! Things change.

She prefers marriage in the States and maybe I'll try for a second K1 here. I don't want to risk a (bogus) Waiver refusal, since I shouldn't have to ask for a IMBRA waiver in the first place. So I lean toward Cyprus. We haven't decided. I think we'll decide when I return to Novosibirsk in September/October.

hey, it is possible to do CR1 after K3. You simple complete the process through NVC as you would without K3 and it'll all be okay.
If you have questions, you can PM me, I did it that way and it was way faster than AOS.

But you wouldn't have to apply for advance parole with K3 anyways, as it is a multiple entry visa which does not require AP to travel to and from the US.

Good luck