Due to my failing memory (degenerative), I am in love with Due for iOS, and I at least appreciate it on macOS, despite it being less elegant to use than iOS, and that the macOS version is in need of an update and some love. I especially love the fact that it is in total sync across all my iOS devices/Macs.
It can even be used in conjunction with Reminders (or not; you can select some or all or none of your Reminders.app lists to also appear in Due); one of my favorite features is I can set Due to scan and “capture” Reminder events added to a particular list; in my case, I set it to the default “Reminders” list in Reminders.app; this way, I can say, “Hey Siri, remind me to do that thing with Dave tomorrow at 10:15AM”, and Siri will oblige (without the frustrating frequency of failures if I also try to designate a particular list to which to add said reminder); then Due grabs that item from Reminders.app and it becomes a Due item, where I can later add snooze, repeat, custom times, retitling, logging, etc.
If I say, “Hey Siri, remind me to do that thing in two minutes”, Due will grab it and its own Notification will then promptly appear, and from its notifications options, I can then quickly add all the details/snooze/sounds/repeats/etc. as desired.
Due also has Timers and Alarms, but I don’t personally need those as much; but when I do, I find them pretty feature-rich.
It does everything you ask for, with one exception: large, in your face, persistent notifications on macOS (the default is standard Notification Center flags); however, if you simply combine it with Growl for Mac (yes, it still works), you can choose a Growl notification style that is to your liking. I personally use ‘Music Video’ (don’t let the name mislead you) which produces a large banner that pops up across the entire bottom of whatever display I select. Growl also has many options to customize each notification style (color, opacity, style, font, duration, persistence, etc.); and even more fun, Growl will let you select a different style/theme for every app you choose to display with it. You can slect from a plethora of ready made, downloadable themes, or create your own. It’s even super easy to take one you like and use it as a template to tweak for every different app/use you can think of,
Growl will further (optionally) display a ‘missed notifications’ “Rollup” window anywhere you like, and can be optionally set to only appear after you wake the screen, to see what events you missed while you were away. The “Rollup” is customizable to always include or exclude certain events or apps so it doesn’t get too crowded.
Sadly, Growl is seemingly no longer under development (for most people Notification Center is good enough, and NC is essentially a Sherlock of Growl in the first place), but, again, it still works fine for every app that still supports it (and you can even manipulate other apps into supporting it via AppleScript).
Another alternative to your notifications complaints with stock Reminders.app might be to deploy some pretty basic AppleScript or Automator; as part of both Reminder and Event Alert options (bizarrely only visible in Calendar.app), you can optionally choose the type of Alert (“Alarm”) you wish to receive (Custom… -> Message, Email, File, Location, etc., ) and from there you could use it to trigger an AppleScript message or Automator popup which would appear dead center of your screen (in addition to as many other alert/alarms you also wish to receive).
Third party utilities like Keyboard Maestro and GeekTool, which also have floating message/object display capabilities, could be employed to pick up Event alerts and generate more visible displays of reminders that are persistent as you desire, as well.
There are probably other solutions; I’m happy to continue the conversation if you have questions.