Problem creating subscriptions on Replication Server version 15.7.1

I'm going to outline a T-SQL way that uses most of what you already have.

1. Create a table to hold your publication information (for the solution that I have written, it's just the name of the publication and an identity column)
2. Create a table to hold your subscriber information (in mine, I have name of subscriber, subscriber database, identity column, and a column that references back to the publication)
3. When you want to create a new subscription, you put a new row in the subscriber table with the relevant information
4. In your "add subscription" script, do a left join between your table and syssubscriptions to find out what subscriptions are in your table but don't yet exist. Run a cursor over that info and for each subscription that doesn't exist, create it.
5. After you're done adding all of the subscriptions, call sp_startpublication_snapshot for each publication that has uninitialized subscribers.
6. Fin (aka "you're done").

In the end I simply did what the server wanted, i.e. created all the "publication" tables (*dbo.MSpeer_** and *dbo.sys**) in the problematic database (the one that was the publisher), through Script Table As -> CREATE To dialog. Thanks to this server allowed me to disable publishing and distribution. Then I only needed to reconfigure replication.

Hope, next time it crashes (actually I hope it won't), we'll be wise enough to backup tables involved in replication thoroughly.

Additional information by Zane, originally left in a comment:

The tables dbo.MSpeer_* and dbo.sys* can also be created by configuring the distributor/publisher on a different server with SQL Server installed. This will create these tables in the database that you've set for publishing. See -> Tables - >System Tables in SSMS.

Then, generate the schemas for all these tables and then create these tables in the problematic database which will allow you to disable distribution and publishing and reconfigure the distributor.