Coming back to the original post, just sell the shares at Computershare, pay the fees, and re-buy them at your discount brokerage if you want to own those shares again.
Computershare is an archaic way to own stock and makes it way too complicated and expensive for retail investing.
My case was like the OP's - shares bought as a DRIP plan by Grandparents and parents starting when I was a baby and let the compounding work its magic. I had 50-odd certificated shares of Bank of America that I didn't want to sell quite yet (during the recovery, after the recession), so I transferred them from Computershare to my Fidelity taxable brokerage account. Big mistake. This involved multiple phone calls, printing, signing and mailing forms via post, etc etc. But the biggest pain in the arse was recording the cost basis of those shares in my Fidelity account.
My dad kept all the statements so this had to be done manually, for each and every transaction and dividend reinvestment, by looking through 30+ years of statements from C&S, NationsBank, and Bank of America.
I am so glad to be done with Computershare.