Neutron Highway, nuf said.
With Engineering and a purpose built ship and a route pre-planned its 1hr 47min. I know, I did it -
https://forums.frontier.co.uk/showthread.php/374560-Evacuation-Proclamation!
Caution next bits involve maths <- All been fair warned!
Worst sensible case:
Without engineering in say a 28ly Asp explorer (which seems a fair range to me if you put A grade core internals and fill up most modules). With that range Spansh says 384 jumps to route there. Settings are Sol->Colonia with 28ly jump range and 45% efficiency In case the link doesn't work right.
https://www.spansh.co.uk/plotter/re...80?efficiency=45&from=Sol&range=28&to=Colonia
Lets round up to 425 jumps (+41) and be really generous saying you have lots of diversions for fuel or whatever. And lets assume 1.5 minutes per jump once you get into the swing of neutrons. <- I averaged ~60 seconds per jump so 90 is more than reasonable to average over a trip where you should get more and more proficient with them.
That makes the
worst case 637.5 minutes travel time or 10 hours. Both ways thats 20 hours flightime.
Best sensible case:
Realistically you can probably push an Asp with a class 5 business passenger cabin to 33ly odd. Same set-up on Spansh gives 324 jumps. If you hit it optimal only refuelling when necessary you add 23 jumps on. 450 lets say. If you optimised for the 1 minute per jump time I averaged thats 7.5hrs travel time. Or 15hr return trip.
Summary & General advice:
Truth is it's probably somewhere between 15 and 20hrs flight for a non-engineered ship doing the highway. Without the highway in even a 33ly ship you are looking at 790 odd jumps which is 13hrs per way time or 26hrs total return trip. Easily possible in 3 weeks for hardcore gamers who rack up 5+ hrs every Saturday & Sunday and a few hours in the week but as you say a heafty playtime isn't something everyone can afford..
A single engineer modification to G5 range modify the FSD will get you to 49ly ish. That again in spansh now changes it to 173 jumps, adding the 25 odd required fuel stops in lets make it a round 200 jumps which equates to 3hrs 20min each way at 1min per jump. Or ~7h return trip. Easily possible in a weekend.
This massive change is because neutrons multiply range by 4 which means every 5ly you squeeze out your ship actually gives you 17.5ly bonus per jump averaged out.
In short it's probably worth spending the perhaps 5 hours required at Farseer for a good G5 FSD.
Generally my advice to everyone doing long range passengers is hot foot it out, get a big play-session or two lined up before you pick up the missions and aim to get all the way to your target destination within a day or two. If you see interesting sights then bookmark to come back on the return trip. Take the hit and spend the time travelling. I generally start Sat AM and do maybe a 3-4hr playsession. I'll do the same Sunday and usually be at my destination.
Then I have 2 weeks 5 days to do the return trip and I can simply look at the distance to Sol and calculate how much I need to do per day to make it back in time. In this case 26kly over 19 days means I have to travel 1,368Ly per day to keep pace. I'd aim conservatively for 2,000ly per day so that I'll be home in 13 days. Gives me 6 spare for mishaps and whoopsies.
TL: DR
To answer the title yes its fairly easily possible but no its not without the hours to commit. (90min ish per day on average required for 3 week duration)
Using the neutron highway drastically reduces the time taken by anything between 25%-45% making it manageable for those with less time to give. (45-60min per day on average required for 3 week duration)
Using both the neutron highway and FSD engineering reduces it by anything up to 75% making it manageable for even those with very little time to get in game. (25min per day on average required for 3 week duration)