I came with a K1 visa in 2016 fro Germany for the same reasoning, to be together quicker. I would never do so again. The adjustment of status process after the K1 in the US is an expensive and timec-consuming mess during which you cannot work, drive or travel. For someone who lived a completely independent life prior to moving, being completely dependent on my spouse for months was pretty harrowing. And back then things were much quicker than they are now, I had my travel & work permit in about 3 months from filing and the Green Card 2 months later.
These days things take MUCH longer and you are stuck in this horrendous limbo. If you plan on getting married anyway, do so and file the CR1. It is cheaper in the end and will make your start in the USA much easier.
Not sure what the point of the DV would be? As a US citizen spouse you are guaranteed a green card, no need for DV...