I bought my Timbukt2 messenger bag in 1998 and it is still going strong. Being an old one, it had no bells or whistles, just a single big compartment, but the new ones have dividers, pockets, etc. My bag has been effectively waterproof, the material is completely impervious and the flap coverage is good, so water doesn't get in, even in the Portland rain. You might want to wrap your food/liquid containers in gallon ziplock bags to protect your books against spills. Find a zippered pouch that fits on the strap, that gives you the easiest access to phone, wallet, keys, etc. I'd get a custom one with a big reflective center panel, and the custom bags are made in the USA. Sounds like you carry enough stuff that a large size would work well.

I recently switched to an Ortlieb backpack because I started commuting on a drop bar road bike and as my torso position got lower (when I'm in the drops, my back is at about 15 degrees), the messenger bag tended to fall off to one side or the other of my back when heavily loaded, despite the stabilizer strap. This was never a problem on the previous bikes where my riding position was just slightly more upright.

I've used Ortlieb panniers before, and they are clearly the best way to carry things for a long ride, but if you are on and off the bike often (commuting, errands), I prefer to be able to simply get off the bike and walk away, instead of unhooking panniers then having to carry them around with my hands full. There is a reason why messengers don't use panniers.

P.S. I just noticed the custom bags are currently 20% off so a large or medium would be pretty close to your budget. I have no connection w/ Timbukt2, except for buying this bag many years ago.