As for the election, it is possible to hold a regular meeting with a quorum. At that meeting the assembly could, in this order:
1. Suspend the rules to permit only the election to come before the assembly.
2. Set a time for the polls to open and close.
3. Recess and let the voting begin. Stay in recess until it is time for the polls to close.
4. When the voting ends, and the call the meeting back into session, announce the results and adjourn.
3 and 4 can be cone using an adjourned meeting. This will, at least, limit the exposure time.