How to upgrade from Windows 10 Home without product key to Pro

So, being the dummy I am, I installed Windows 10 Home over Windows 7 Pro. Right now, Windows 10 Home is unactivated because I can't use my 7 Pro key to activate 10's Home edition (I get error code: 0xc004f210 You are running Windows 10 Home. The product key you entered cannot be used to activate this edition.) I found that out through a call with Microsoft -- after we find out I'm trying to use a Pro key on a Home OS, I ask them how I can upgrade my current version of Windows 10 to pro. They tell me to clean install Windows and enter the Windows 7 Pro key at the beginning of the setup (I had initially skipped all of that and waited to activate after Windows 10 was installed)

So, I go to do a clean install off of the USB installer (really old version of Windows 10 that I had laying around from when I initially upgraded my laptop soon after Windows 10 was publicly released). I hit the "enter your product key" right after I select my language (before I select which drive I want it on), and enter my Windows 7 Pro key, but get the "This product key didn't work. Please check it and try again." error.

My first thought is that I should probably download the latest version of the USB installer, and I'm downloading it right now, but that's going to take forever (> 1 day by the looks of it) with my slow internet connection. I'd also have to re-download all of the updates I finally got done downloading for Windows 10.

My question is: Is there some way I can upgrade from Windows 10 Home to Windows 10 Pro, without having to do a clean install, from the Windows store or something without entering the product key until after I upgrade? If I try to enter my 7 Pro key in the store for the "I already purchased 10 Pro let me enter a key", I get the same error:0xc004f210 "You are running Windows 10 Home. The product key you entered cannot be used to activate this edition" I do when I try to activate Home with my 7 Pro key.

Edit: The Windows 10 Home edition I'm running right now is up-to-date using the current version 1511 build 10586.71

The reason you cannot use your Windows 7 Product key to activate a new installation of Windows 10 Pro is that this functionality was only added in Build 1511, November 2015, as mentioned on this page:

Starting with the November update, Windows 10 (Version 1511) can be activated using some Windows 7, Windows 8, and Windows 8.1 product keys. For more info, see the section Activating Windows 10 (Version 1511 or higher) using a Windows 7, Windows 8, or Windows 8.1 product key in this topic.

As such, you will need to use the latest build, as you have discovered and are now doing. The only way you will be able to upgrade to Windows 10 Pro without a clean install would be to first install the 1511 update and then use your Windows 7 Pro key.

I'm not sure which way would be quicker for you, but any build previous to 1511 won't accept that licence key.