I had the same/similar thoughts on this topic recently and came to a concept that works for me (props to -ck for "the rock with the toothpick" image)
Think of solo mining as drilling holes into a huge rock from either side, desperately searching for a single fragment of gold inside. The one who finds it first, may keep it.
The drill is your miner instance. The more hash power you have, the bigger and faster rotating is the drill. There are MANY MANY drills, that are drilling this poor rock all at the same time.
Now you can drill holes sequentially with a bigger drill (by combining your hashing power into a single miner instance). Or have multiple holes drilled in different locations on the rock at the same time, but with a smaller drill (by splitting the hash rate on seperate miner instances).
Each mining instance gets the location info on where to drill with the nonce and extranonce1 value from the solo pool (or bitcoind) and drills there for gold until the self-generated (and continuously incremented) extranonce2 value is exhausted. Which then means, your miner did not find the gold in this location. Then the miner requests a new location and starts drilling there again. The number of locations is near to infinite, so a chance of a collision is near to none. Exactly this drilling job is repeated all over again and again until the gold is found by someone.
The most tricky (and hardest to understand) aspect here is that, while the very same location might be your drill's sweet spot, other drills cannot find anything there. So reusing the same location is not a bad thing in general. (This is due to the fact that each miner creates a different unique input for the hashing.)
A bigger and faster drill will increase your chance to find the gold earlier since you can drill many more holes than others in the same time, but even the small drill next to yours may be the lucky one instead. It's all pure luck in the end, with a known probability though, which may lead to you finding the block in the next instance or never.
All the experts out there, please correct me if I am wrong ofc