Sounds like your SaaS provider needs exactly what I am offering at the new visualSilicon.com
I do all my work on Gmail. So I have a couple of notes. It can certainly be improved as an inbox for the working professional, but it is indeed the best email client I can get my hands on.
The link you shared has a lot of what you are asking but I would say you have to see what works for you because everyone works differently. For example colouring labels works really well for me but some people might not like too many colours…
I didn’t see them mention the Snooze feature. It’s a god sent feature. Just snooze your sent or received mail to when you want to followup and forget about it. Saved me a lot of headache. It goes into snooze folder and reappears at the date and time you picked.
Regarding the points on that page also the “stars or those arrows” are not great for me, I ended up having so many of them that they have become somewhat meaningless. I use labels (folders) and colour them with light or strong colors instead. Strong red has the highest priority. When I want to see highest priority stuff I just click on that label/folder and I have a list or I easily see them amongst hundreds of emails. What’s great is you can have multiple labels (priority, which customer, and even which stage of work)…
And don’t underestimate the power of automatic filters. You can automatically label emails with certain senders and subject lines (which gives you colouring out of box) and in case of less important stuff you can “Skip Inbox” so you never see them until you choose it is time to click on that folder to see them…