Ben,
If the 75-300mm lens is having kittens trying to focus on the Moon, then, I think your only option is going to be: rough focus; take a shot; inspect image; focus; take shot; inspect image; focus; take shot; inspect image, and so on.
A lot of us DSLR astrophotographers use software, such as DSLR Focus (which is pretty much now defunct and has no support for newer cameras) or DSLR Shutter, which allow you to program multiple exposures.
To attach the camera to the telescope, you will need a T-adapter and a T-ring for your EOS camera. You might also need an extension tube to bring the image to focus.
Bintel stock these items.
Examples:
https://www.bintelshop.com.au/Product.aspx?ID=5439
https://www.bintelshop.com.au/Product.aspx?ID=5551
https://www.bintelshop.com.au/Product.aspx?ID=7082
Email don AT bintel DOT com DOT au
He'll guide you in the right direction.
Hope this helps.
Regards,
Humayun