I'm obviously missing something here, which of course wouldn't be a totally new experience. I believe you have mentioned that the border is transparent. Therefore, when you look at the border in that file it is not white, but a white and grey checkerboard pattern, correct? If that's the case, why not fill the border with pure white and see what happens when you print it. If indeed the border does appear to be white, then obviously it is not transparent. Also, if the border in the file "appears" to be white, use the Eye Dropper tool and take a measurement of that border. Open the "Info" dialog and check the RGB numbers. If they are anything but 255, 255, 255, you do not have a pure white border. You can also use the Digital Color Meter, which you will find in Applications > Utilities. That will also determine if the border is indeed pure white. However, I believe you have determined that the whole image has a very slight color cast, which of course can be corrected in PS or LR. If the border has any density at all it will definitely pick up that cast. I would suggest that you do a selection of the border and fill that selection with pure white. If that's not an alternative you want to approach, perhaps get the digital file of the original and place it on a pure white background to produce the border you need.
In reference to the crop marks. Since most of my work is done in PS, I'm not totally familiar with how LR would handle that. I do not like the crop marks in PS, so I simply add a one pixel black stroke inside the image and crop to that. Works great!
Gary