I think in this day and age the best approach is to take a video of everything (showing models and serial numbers), then upload it to the cloud (Google Drive, Evernote and Dropbox all have free tiers, as do others, so there's no excuse not to!).
If you paid originally with a credit card (or bought from a music store), there's a chance they could get you at least some proof that you bought the equipment that was stolen.
I'd get the word out to the local music stores too. Someone might overhear something. Musicians may not agree on lots of things, but they will team up against a gear thief!
I have some music stuck in my head, but I've yet to find a device that adequately connects between my head and a DAW... I've tried some methods, but the results were subpar! Maybe I need to get one of those new HDMI 2.1 ports embedded in my head, ya?