RDP client connection experience to AVD in shutdown state

We use dedicated per-user AVDs and as with most scenarios, we shutdown our AVDs if inactive for 3 hours. What we have found is that logging-in experience to an AVD in shutdown state is quite poor and I am not talking about the time needed to start-up the AVD. It's other things that are annoying as listed below. Is there any settings we can change to improve it?

- RDP client is too sensitive to mouse clicks? Sometimes an impatient user clicks their assigned AVD multiple times in RDP client resulting in multiple parallel connection attempts. Client should detect that a connection is already in place and not initiate another.

- User gets different kind of errors and need to try the connection again. Some examples of errors our users are getting are "This computer cannot connect to remote computer. Error code 0x704", "We couldn't connect because there are currently no resources available" .

As noted above, we don't use multi-session and instead all our AVDs are dedicated per-user session hosts that are simply shutdown after a certain period of inactivity.