jgold,

If you are on a booked rtw ticket, you may also need to consider what is involved in "regiggering" your ticket. Change fees and reissuing for rerouting may involve some time and hassles. If you have not yet booked, this may be less of a consideration.
FWIW, my experience with LAN is that the value of the business class check in varies substantially from station to station and for specific routes. LAN is reasonably well organized for check ins and there may not be all that much to be gained, especially if the ticket adjustment only advances your qualification by one or two trips.
Not all the variables to consider are presented in your post, but what is involved in the "regiggering" needs to be weighted against the benefits achieved.