One more piece of info needed ... is the old account in Q still connected to the old Firm?If NOT, then just 1) take a backup2) rename that old account to the new name,3) delete the newly created account4) connect the old account (now, the only account) to the new firm.By doing this, all of your account info stays in one place. After all, to you it's all one account ... it's just the brokerage that changed.
In the old account, you can simply manually add a "Remove Shares" transaction for each security to bring the share balance to zero. You also would have to manually add an Adjustment transaction if you had a cash balance. Doing this for all your securities and cash would zero out the account. (Note: depending on your particular situation, adding such a transaction might create a placeholder that offsets your transaction-post back if you see adding the transaction doesn't zero out the balance.)This will preserve the cost basis and lots in the old account, but keep the balance zero. (I don't know how much history the new online firm provided and if that will conflict with your older data-you will have to determine that.)