the answer is in your own question, "we don't want to impact the fail over of the production database if something goes wrong with the fail over of the monitoring...

stop the cluster service on both nodes, then start sql server from sql configuration manager and see if you can start the sql, post the sql error log if you...

(any execpt primary) .. thats why i said play with the code

to make it more clear to understand.. 

-- restore full file group primary
--MUST RESTORE...

check/fix  permissions on the new drive

off course you can, play with the code. 

CREATE DATABASE [test] ON PRIMARY
( NAME = N'test', FILENAME = N'y:\tmp\test.mdf' , SIZE = 5MB , FILEGROWTH...

i suspect some records might be with different page code, it usually happens when you change you database collation while data is in tables. I suggest try specifying page code...

make sure sql server name is not longer then 15 chars.. check SCMS documentation.

check tcp/ip is enabled on both servers. 
talk to your network admin, and open 1433 between both servers

do you have permission on cluster, delete the resource or role .. or have sysadmin do it for you.

my guess is you are missing login in the sql server..

remove the database from BAG from both or all nodes and then add again, you can not move a group to a server where there is no database

As I understand the error, the certificate is either missing or different , can  you match thumbprint from error with thumbprint in sys.cetfiicates

you may want to consider Sql Server Management Data Warehouse, you will get more then you are looking for and its ease and free.  https://docs.microsoft.com/en-us/sql/relational-databases/data-collection/configure-the-management-data-warehouse-sql-server-management-studio

modify this.. 

-- choose database or currently used database will be selected
DECLARE @db_name VARCHAR(100)
SELECT @db_name = DB_NAME()

-- Get Backup History for required database
...

good luck
 http://windowsitpro.com/powershell/changing-service-credentials-using-powershell