If you are looking to completely revise how you use email, I am sure there are 100 ways to accomplish it (and some suggestions here are helpful). However, it seem like the current system is working fairly well for you (and your colleagues) and you just want to streamline it somewhat.
You can do this by using Gmail with their "tags" but, more importantly, the ability to never have to delete anything and search everything.
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Simple answer to your question - Yes, use Gmail.
If you are looking to completely revise how you use email, I am sure there are 100 ways to accomplish it (and some suggestions here are helpful). However, it seem like the current system is working fairly well for you (and your colleagues) and you just want to streamline it somewhat.
You can do this by using Gmail with their "tags" but, more importantly, the ability to never have to delete anything and search everything.
Good luck!