This is exactly what we did. It was significantly easier and it was definitely cheaper. Yeah, you want to begin your life together, but if it's a short amount of time, well worth it IMHO. We crossed into the US 1 day after our 1yr anniversary and received those 10 year greecards, even though our temp I-551's in the passports said CR-1/CR-2 (I have kids that were minors at the time).
You have plenty of evidence, so don't stress about it. Having the actual boarding passes and other evidence of actual time spent is hugely helpful. I wouldn't stress about photos too much. If you had a nice wedding, excellent and sounds like you have nearly all of what you need from that alone. I wouldn't stress about a bank account, either. You can, however, list each other as beneficiaries on life insurance, pension policies and other long term, not so easy to change the beneficiary accounts, which definitely lean towards the side of serious, long term commitment from an outside viewer looking in.
I don't blame your wife for not being transparent on socials. People are ugly out there and don't need to be all up in your business. My hubs isn't on socials other than LinkedIn and then my oldest got him watching TikTok videos; he's a shadow lurker by nature. I keep my own profiles locked down and don't share a lot myself. People that are invited to know, will know! We work at the same place and many people had no idea for years that we had dated, let alone gotten married. One of my colleague friends didn't clue in until she showed up at our house to borrow a ladder LOL! She assumed it was just my house.
File taxes as married, filing separately as you'd stated, and get that I-130 filed.