If it's any consolation, I haven't found a system that I'm super happy with either.  With a varied client base I just kind of roll with the punches.

I try to have certain days per week for certain tasks.  One day may be client meetings (today for example, I'm open until my 3:30 shows up so figured I'd get caught up on the forums and some emails).  The next day may be zero client meetings but working on mail-ins.  Another day might be printing out all of the uploaded docs (yes, you can make fun of me for this but I LIKE PAPER and have a ton of scratch paper that I can print on the back of!  I can put it in whatever order I want, make tick marks on it, even do math on it for things like mixed-use mortgages.)  Another day with my review hat on.  Another day for clearing open items and (hopefully) finalizing returns.  This process really only works for weeks that have at least 12 days in them (thus the "not super happy" part).

Set expectations.  I'm telling my drop-offs today that I'm working on about a 3-week backlog so they might not hear from me for a while.  At this point I still expect to get things coming in now out by 4/18.  Shortly that expectation will change to "I'll take a look when I have a chance but we'll likely need to file an extension this year, I'll let you know if you need to make a payment by 4/18."  Then the "My 4/18 pipeline is already full, here's cut/paste instructions on how to file an extension on your own with IRS DirectPay.

Rick