Restore a SQL 7 database into SQL 2014 without in-between versions?
If I was in your place, I would go the below route which is not as tedious as you would think of.


Backup your sql 7.0 database and restore it on sql server 2005.
Backup your sql server 2005 database and restore on sql server 2014.


Its a myth that you cannot upgrade a database to a version more that is more then two versions newer. 

I have written an elaborated answer about the pre and post migration steps that will be a handy reference to you.

For automation, you can use dbatools (powershell based) - start-sqlmigration that supports migration from sql server 2000 to 2016 (newest version out).

Note: You have to test out a lot of stuff as this is a major leap for your application !