From your advice, it seems (am I right?) that I can carry out your steps 1 & 2 and then ask the ISP to install WP into a chosen new folder in my server - and start again?
My actual advice is still to contact your hosts support group...
However, at your request, and believing that it was your intent to do it yourself without involving your ISP, I pointed you to the installation instructions and listed the 2 things you need to do to completely remove WordPress from your server, in order to start over with a fresh database and fresh files.
I was rather hoping I might be able to simply use ftp to remove specific files/folders and replace them with clean ones.
And that's what you would be doing. How to upload the WordPress files is one of the steps described in the Installing WordPress instructions.
One of the reasons I keep urging you to contact your hosts support group, is that they initially installed WordPress for you, and only they know what they did during the course of that installation. Checking with them first, only seems prudent.
If after reading the installation instructions and requirements, you are still unsure if it is something that you want to tackle on your own, call your hosts support team and tell them that you have some concerns, and would like to start with a fresh WordPress database and fresh WordPress files. I should think they might be willing to give you a hand with starting over if you ask. Beyond that, I'm not sure how else to point you in the direction you want to go.
 The one file you should make a copy of and save locally in a safe location at this point, is the wp-config.php file. It contains all of your database connection information. I will assume at this point - because your ISP installed WordPress for you - that you may not be aware of the database connection information that is in that file. It would be a good idea to save a copy for future reference. Good luck to you!