So, I've been very curious to review how the Tamron 150-600mm f/5-6.3 SP Di VC USD would work with a teleconverter. Today I tested it out on some lunar photography using the Tamron 300F-FNs 2x. Here are the sample images from tonight (and last month without the converter). Take a look, and then I'll share my thoughts.
As you can see on the image using the Tamron 300F-FNs 2x teleconverter, you definitely get that extra reach you are looking for in lunar photography, but the important question is are you getting the detail.
As far as detail goes, you are getting just a bit more with the extra focal length. But, you are not getting the full power of twice the magnification. As expected, the Tamron 300F-FNs 2x brings a loss of sharpness that reduces the benefit of increased zoom.
Watch-out, what you give up is auto-focus. On the Nikon D750, auto-focus disappears when you take the lens out past about f/5.3 - not very useful if you're looking to double your 600mm's of zoom. But, with some careful Live View focus, you can achieve pretty sharp images.
But, here's where the real fun came in. After taking about a dozen photographs of the moon, I did a rough alignment in Photoshop and brought them into RegiStax V6. Re-aligned them and processed them to get this beautiful image of the moon utilizing the full 1200mm of the Tamron 150-600 plus teleconverter.