Enabling SSL for all pages when the store is in a subdirectory - duplicates subdirectory name

I have a nopcommerce 3.0 store in a subdirectory (application) of the site, and that works fine:

mysite.com/mystore/

I've installed SSL certificates on the site for mysite.com and www.mysite.com, with redirects in the site web.config to force everything to https://mysite.com .  That works well for pages in the main site.

Now, I'm trying to set up the store to use SSL, and am running into problems where it is adding "mystore/" to urls that already have it.  For example, the link to the public store in the admin area points to https://mysite.com/mystore/, but when I click it, it goes to https://mysite.com/mystore/mystore, which of course doesn't exist.

What I've tried:

Under General and Miscellaneous Settings, Security Settings tab, check "Force SSL for all site pages".

Under the Store settings, I've got:

Store URL: http://mysite.com/mystore/
SSL Enabled: Checked
Secure URL: https://mysite.com/mystore/

This combination ends up duplicating /mystore/ in some of the links, including when you type https://mysite.com/mystore/ directly in the browser - it goes to the "page not found" of https://mysite.com/mystore/mystore/

Once there, clicking on a category link works: https://mysite.com/mystore/mycategory , but the images on the pages don't show because they are being looked for in mystore/mystore/content.

Any suggestions?

Adding:  I reversed all those settings, cleared cache, restarted the application - and the symptoms remain.  Somewhere it is storing that it is https and adding /mystore/mystore/ to some of the pages/resources.  So, I can't even get back to a working non-https store.

Also, a correction to my first post:  The nopCommerce version is 3.6, not 3.0.

And one more result: after reversing the settings, the non-https store was working normally in a different browser.  I cleared browser cache, and my main browser is now working.

Still left with: how to I put the SSL settings back in without breaking the store?

More information.  If I try:

Under General and Miscellaneous Settings, Security Settings tab, check "Force SSL for all site pages".

Under the Store settings:

Store URL: https://mysite.com/mystore/  (Note the https, not http)
SSL Enabled: UNCHECKED
Secure URL: BLANK

I now have a store that works with an https address, but it will not force an https address.  If you enter the store typing http://mysite.com/mystore/, you'll remain as http.  If you enter the store typing https://mysite.com/mystore/, it remains https.

And finally, I left the above settings, and added a rewrite section in the store's web.config to direct http to https.  (The store itself takes care of www.mysite.com to mysite.com)

So, to make it work with the store in a sub application folder, it's done by setting https as the store's main url, not setting a secure url, not checking enable SSL, but do set Force all pages to SSL (haven't tested if that is needed), and add a rewrite rule yourself in the store's web.config to switch http to https.