Backing up SQL Server 2008 database in different recovery model
For example, the .bak file reads 14GB but due to the transaction log the file is actually 60+GB.


Your problem is an inadequate maintenance and backup/recovery plan. You are not taking log backups with enough frequency, this is why your log grows through the roof. Start taking log backups to allow truncation and then shrink the log. You'll have a better recovery plan and a smaller database log file.

As for the question: no, there is no way to change the restored database file size(s). The restored database will always have the exact same layout as the original backed up database. Recovery mode has nothing to do with this, your restore would need 60GB on any recovery model. You're only mixing the recovery model in the discussion because you shrink the log by switching to SIMPLE. Read the linked article for more details on this aspect.