Not sure I agree with your information that SGC won't up-grade a card submitted for crossover.
This is from the SGC website's FAQ:
http://www.sgccard.com/submission_FAQ.htm
Q.) Does SGC accept cards graded by another company to be crossed over?
A.) We do offer a crossover service that reviews cards graded by other grading companies. All crossovers must be submitted under the appropriate service level according to the value of the card. Crossovers may be submitted along with raw cards at any service level. Turnaround times on crossovers vary based on the service level chosen.
The procedure for submitting cards for crossover review is easy. Simply fill out an invoice for the appropriate service level desired, and list each card notating the required minimum grade you are looking for in the ‘Variations Or Comments’ column on the invoice. You might also want to stick a post-it note on the slabs notating the minimum requirements you are looking for.
You have several options when it comes to crossovers. Whichever option you choose must be clearly listed on the invoice. We can evaluate cards for the same grade or higher, for a higher grade only, for a lower minimum grade, for any numerical grade, or we can crack the cards out and regrade them entirely. The latter option would allow for the ‘Authentic’ designation in the event our graders detect trimming or other alteration on the card. If you have any questions concerning the crossover options available, please feel free to call Customer Service at 1-800-742-9212.