Is it normal for multi-color prints to need this much cleanup?

Some cleanup is just part of multi-color, but the amount you're describing sounds like it can be cut down a lot. The strings and blobs along the edges are mostly ooze from the nozzle sitting hot during the swap. Z-hop won't touch that because the material is already leaking out before the head ever moves, so you were right that it did nothing. What actually helps is turning the swap itself into less of a mess: in the slicer look for the purge or prime tower settings and try trimming the purge amount down in small steps until you see the colors just barely come out clean on the tower. Most people over-purge by default and every bit of that extra has to go somewhere, usually onto your model or into that ring where the tower meets the base.

Also check if your slicer has an ooze shield or wipe option for multi-material prints. A thin shield around the outside catches the dribble and peels off with the model instead of you picking at corners. Dropping the printing temp a few degrees helps too, since cooler filament oozes less while it waits during a change. Just go slow with that so you don't lose layer bonding.

On the second nozzle, I'd leave the height alone. Messing with one nozzle's offset relative to the other usually causes more grief than it solves, dragging on one layer or printing in the air on the next, and then you're recalibrating everything. The problem isn't nozzle height, it's ooze, and ooze is a temperature and purge problem.

One more thing that made a real difference for me: dry filament. I didn't believe it either until I ran the same two-color job with a fresh spool and the stringing dropped by more than half. Damp filament swells and bubbles during those long hot waits between swaps and it makes the strings way worse.

As for the picking at it with a hobby knife part, yeah that never fully goes away. I keep an old toothbrush and a pick set next to the printer and do a quick pass while the bed is still warm, everything comes off easier before it fully cools.

One thing that cut my cleanup way down was grouping the color changes. My first big two-tone job had the slicer putting swaps all over the place, sometimes only a few layers apart, and every extra swap was more junk on the sides. I went into the layer view and moved the color change markers so each color ran as one solid block. Fewer swaps, way less scraping. Took ten minutes in the slicer and saved me an hour with the knife. Might not work for a castle gate depending on the design, but worth a look at where your swaps are actually landing.

One thing I'd add is to keep a little note of what purge settings work for each filament combo, because I found the amounts that give a clean transition on black-to-white are way too much for somethig like gray-to-gray, and I was re-tuning from scratch every time until I started writing it down. diferent colors and even different spools of the same color seem to need slightly different amounts, which annoyed me at first but it does make sense once you think about pigments. After a few prints you basicly build your own reference sheet and the tuning stops feeling like guesswork.

Seconding the dry filament point. I started keeping the spools I use for color swaps in a sealed tub with a couple of those little silica packets, and the difference on long jobs was obvious. Before that I'd get these fat drips right at the start of every change, now it's mostly a thin wisp that wipes off with a thumb. Cheap fix too, the tub was leftover from holiday storage.

I'd push back on trimming the purge way down though. Chased that same advice on a print last month, kept shaving the purge untill it looked clean on the tower, then found the last half of the model had the colors bleeding into each other faintly. The tower can look fine while the nozzle still has old filament inside it. Now I'd rather waste a bit more material than toss a twenty hour print. So if you do cut it back, do it slow and check every color section, not just the tower.

Update: moving the color change markers around so swaps landed on fewer layers cut the edge junk down a lot, so that tip alone was worth it. Still stuck with the ring of purge material where the tower meets the base though. Does the purge tower size affect how much of that splashes onto the print, or is that just placement?