Hopefully the following will clear up some of the questions in this thread.
Prospective elders are assigned to the high priests group by default. The bishop should determine whether a prospective elder is best served by being assigned to the elders quorum or high priests group. For more details on this, refer to
Handbook 2 section 7.6.1 and the First Presidency letter dated 3 November 2004 regarding responsibility for prospective elders.
Class assignments for wards (and branches) using Leader and Clerk R 3.0 are handled in LCR. Once a unit is upgraded to LCR 3.0, configuration information is sent to MLS that turns off the ability to modify callings, classes, class assignments, and home and visiting teaching in MLS. At that point, the ward must use LCR 3.0 for these functions.
The class assignment changes can be made by users with LCR access. Class assignments do not require any kind of round trip through MLS. Class assignment data is sent to MLS but there are some known issues where MLS may not have all of the data it needs when classes are split in LCR. MLS tries to detect these situations and requests a refresh when necessary.
If a prospective elder is assigned to attend the elders quorum, the class assignment can be changed in Leader and Clerk Resources. The record will indicate that the elders quorum class assignment is not the default class assignment, which is expected since the default class assignment would be to the high priests group. This does not cause any problems -- it is simply an indication that the member has been assigned to something other than the default class.
As mstauff said, the overview and household tabs for home teaching are not based on class assignments. If a family is not assigned the home teacher, that family will be displayed in home teaching lists based on the default class assignment, which means that prospective elders and single sisters will be listed by default on the lists for the high priests group. That does not prevent these families from being assigned to an elders quorum home teaching companionship.
I think I covered it all.