"Looks like Quicken is not designed to handle transfers from one IRA account to another IRA account".
Quicken does not handle such transfers correctly, it treats the transfer of cash into the other IRA as a contribution; but that's not what this problem is about. You can look in your TO IRA account to see the IRA-to-IRA problem.
This is an old bug that affects the withdrawal of cash from IRA's between January 1 and April 15. It doesn't matter where the cash is sent.
See:
https://community.quicken.com/discussion/7849398/tax-summary-and-ira-distribution
I believe you can work around both problems by defining a Quicken Dummy security, valued at $1/share, to be used for cash transfers. In the FROM account, sell the shares of the real-world security and buy shares of the Quicken Dummy security.
Then use the Quicken Shares Transferred Between Accounts to transfer the appropriate number of shares of the Dummy security TO the other account.
If the TO account is an investment account, sell all shares of the Dummy security in the TO account to create the cash - otherwise the TO account will already have had cash transferred to it.