Would SQL Replication prove to be a FASTER option than downloading compressed DB files every time from servers at different geographic locations?
There are couple of options --

I would not suggest to go with replication as you are making schema changes and it will require to reinitialize the whole replication with a snapshot.


Logshipping with standby option: 


Cheap and effective. Works great and less overhead of maintenance.
Things to look out :


If an adhoc log backup is taken, it will break the log chain.
If you take differential backup then make sure you take full backups with COPY_ONLY option.
Your secondary will be readonly - use the with standby option, so you can read from your secondary. See my answer here for more details.


SSIS with incremental load


Refer to SSIS Design Pattern - Incremental Loads from Andy Leonard



If you are using Enterprise edition then I would suggest you to look into AlwaysON Availability groups.