Not sure in what way Computershare were inefficient? They seem to have resolved the issue as they know you are the executor. So they must deal with you. Have you asked them how you can sell the shares?
I'm in the process of being administrator, where there are shares. One letter from a share group UK says the executor can deal with the shareholding, and if the amount is small, below 20K sterling, they will deal with it under their 'Small Estates' rule. You've to phone them up an pay a fee to them for this
First port of call for you should be to phone Computershare and ask them your options, though I'd follow up in writing.
(ironically one of the shares is Computershare, for BofI shares, but I'm not touching anything until appointed Adminstrator)