LAN does status match and after about one month of patience, I was given Comodoro (OW Emerald) status from my UA 1K status. I don't think this came easy as I demonstrated that I was giving LAN steady future business via my current PNRs that I had with LAN and other promising business opportunities. So, when you draft a letter, please make sure to include at least the last six months of your current FF activity, a carefully drafted letter that shows evidence for your future business with LAN, and (if you have these) any booked itineraries that you currently have with LAN.
Now, I have flown two long haul/mid-long haul segments (SYD-SCL and SCL-LIM) and the treatment has been very good (despite some minor hick ups in SYD during check-in). I was given guaranteed seat blocking on my SYD-SCL and gate agents both in SYD and AKL (short transit stop) personally told me at the time of boarding (in AKL at the time of deplaning during transit) that they have blocked the seat (not to mention small business class cabin) for me!

^