So here is a typical spherical panorama image (original is 14000 pixels wide). I rendered my model and the hdri was too close. The background was blurry and out of scale.
Now, to make your hdri look further away when rendered:
Open in photoshop, make the image a layer. CROP OUTWARDS (make sure you scale keeping proportions, so hold shift and alt to crop from the centre of the image). your resultant image should be larger than the original with a blank border. MAKE YOUR NEW BORDER BLACK. The new extended image is now 17000 pixels wide.
If you want to make your image look even further away......just make your black border bigger (again, crop outwards)....This one is 18,800 pixels wide.
You now have complete control of how far away your background will be

IN ESSENCE, YOUR HDRI STAYS THE SAME SIZE.....YOU JUST HAVE TO MAKE THE BORDER BIGGER TO SHRINK IT IN THE RENDER
