Having recently converted from a stand up to a lay down radiator I definitely understand the problem you are facing and you have my deepest sympathies.
When I called the vendor who supplied the radiator he basically brushed off the installation as being not much of an issue, just maybe requiring a 10 or 12 inch extension on one of the coolant pipes. I found his advice to be lacking.
Like you, I had interference and clearance problems with the crossmember and sway bar structure. It took a lot of under the car eyeball assessment and the use of several longer connecting hoses to make things work.
I could share my solutions but I’m not sure they would transfer to your situation. Hopefully others will chime in with their experiences.
Larry