This may be one of those Return of Capital transacations but that has never worked right for me (doesn't go into A&L screen and affect the cost & tax basis)

How should these realized numbers affect my cost basis/initial invstm amount?

As for this transaction, enter it depending on what needs to be affected. Even no cash was received, it could be like a dividend reinvestment. This is where the money is put back in the investment to be added to the cost and tax basis.
So record a charge to the investment asset. Say Yes to acquired investment. Enter zero as the investment amount since no cash was received. Enter the amount on the first line for the investment asset. On the second line enter an offsetting deposit to an income account for the realized income. As for the quantity, you need to enter some number >0 so enter 1 or .001. If this quantity is a problem then just change it in the Asset/Liab Info back the the original quantity.

If this is reducing the cost basis, then enter a deposit for the investment asset. Answer 'Yes' to sold an investment prompt. Enter the amount for the investment amount. Enter zero for quantity. Yes to the 'Return of Capital' prompt. Charge the income on the second line to some income account. Select Ok to end this transaction. But now you have the cash in this journal. Record a deposit to but this cash to some account for the amount of the realized gain.

The unrealized gain will stay in balance with the difference between the cost basis and the balances as long as two of the three are affected. Since cost plus unrealized gain equal the balance, if the one is changed then one of the other two must also be affected to keep it in balance.