New Tracking of Old Account

When you say,  "download the securities and transactions histories for those currently in my account" is the account set up in Quicken for downloading from your financial institution? If so, you could try the following. This assumes you want to preserve the cost basis and transaction history for your current holdings but don't care about the former holdings.

-- Back up your Quicken file in case this doesn't work the way you want

-- Resolve placeholders for your current holdings

-- De-activate online services for your current Quicken account

-- Set up a new Quicken account to receive your existing securities

-- Use Shares Transferred between accounts transactions to move your current holdings to the new account

-- in Edit/Preferences/Downloaded transactions, make sure "Automatically add to investment transaction lists" is NOT selected

-- Set up online services for the new account. Depending on your FI, you may get 6 -18 months of transactions downloaded. Accept only the ones that apply to your current holdings.

Alternatively, you could skip resolving the placeholders and transferring the shares, but then you will lose the transaction history before the time limit of your FI's downloads. You would have to figure out how many shares you held and the cost basis at that time and enter Add shares transactions to get the shares into Quicken.