Outlook delegated inbox

We have 10 users all have newer Dell windows 16gb 256gb at least laptops all users use classic outlook at the moment. they all use two monitors with the laptop

They are all currently in three inboxes one inbox for order inquires, one inbox for orders which is delegated and the one we have issues with and there personal inbox. 

They like to use a inbox as a work queue users find the email they want to work on forward it to there personal email and move the email out of the queue inbox. While using the queue inbox as an archive.  
Everyone has cache turned off nothing is downloaded locally for the shared inbox.

We originally had each user on the team sign into the inbox with the same credentials not best practice but this team started with two people and quickly grew.  We now have users delegated to the inbox we run into several issues. 

The outlook drags with everyone in the inbox
The outlook does not keep kept up say someone deletes an email someone sitting right next to that person would still see the deleted email in the shared inbox. Causing duplicated works 

Delegated inbox moves deleted items to users personal inbox same with sent items. 
Analytics and reporting and archiving is a whole other issue but not what I am honestly looking for help with. 

MSP wants to get users on a mail handler but the team does not want to have another tab open even when an extra monitor was offered. They also do not like the idea of going back in forth between two different inbox systems. " we basically will have two outlooks" 

Team wants something light weight even asked if there was some sort of extension for outlook. 

Storage wise it has a 50gb storage with an online archive archiving takes place every 3 months. the storage stays at 60-80% if it hits 90% or over the inbox is almost not functional. We thought storage and usability corelated but today we had issues at 70% continually. 

I know i sound green please be as brutal as needed my pride is less important than this issue.

In the off chance someone has been in a similar issue would appreciate any insight on how they navigated it and really wanting to learn.