Now that the final optional milestone is unlocked and patch 4.52 unbroke the expedition, the Omega Expedition is the ultimate quicksilver farm until it ends. You can easily get 6000 quicksilver in an hour or less. I was able to finish in 45 minutes by doing the following steps to avoid unnecessary backtracking and moving around.

1. Immediately scan six plants to get the Exobotany milestone and install the scanner upgrade. Scan as many fauna as you can see and various plants and minerals (focus on whatever your scanner upgrade is giving you a bonus for). In total, you need ~135K units to start for microprocessors and eventually another 250K to 300K for wiring looms.
2. Find your ship and repair it, collecting necessary resources along the way. Take off and head to the nearest ice planet. The ice planets have more things to scan compared to the other planets. Scan as many fauna as you can to try and get the Life In All Its Forms milestone and the second scanner upgrade.
3. Build your base to finish the next milestone and refine some chromatic metal from the copper you received.
4. Somewhere between the starting planet and your base planet, repair all but one each of the broken starship and multitool slots to get the Scavenger milestone. You will need the nanites in a minute. The magnetic ferrite and silver are the easiest ones to skip fixing since they are the hardest/most time consuming to get.
5. Before heading to the space station, install the hyperdrive and build one warp cell. Doing this while at your base ensures you have enough resources without having to backtrack.
6. Head to the space station and buy the microprocessors to finish the hyperdrive. While you’re here, buy 3 C-class hyperdrive upgrades (buy, save, reload) with the nanites from the Scanveger milestone. These will give you enough range to make every warp except the last one in a single go.
7. Go to Rendezvous 1-4 and get both the normal and optional milestones, keeping in mind the amount of units you need for wiring looms as you’re scanning.
8. Somewhere between Rendezvous 1 and 4, you need to find a Traveler grave, get the Indium Drive plans, and install it. The earliest you can do this is on the Rendezvous 1 space station. If you pick the correct option when talking to the Traveler, you should get enough nanites to ask where their grave is (reload if you pick the wrong option). Alternately, if you go into the Anomaly with the milestone selected, you can ask Polo where to find a Traveler.
9. Travel to Rendezvous 5 and finish the last two milestones. At this point, you should have 6000 quicksilver. Technically, you could finish the full set of milestones to get another 4000 or so quicksilver, but if all you want is the quicksilver it is much faster to just start a new save and go again.
10. Go to the Anomaly and buy whatever you want from the quicksilver vendor. These items can then be claimed on any other save you want.