Yes and no.
Yes there were a number of overnight sleeper operations and yes the DC-3 started as the DST but as a percentage of the total airline fleet do not think that these aircraft were that significant a percentage of total fleet hours. I could be wrong of course. I would also add that long before the sleeper services started the majority of mail and some freight flew at night. Again as a percentage of the whole I believe that this was not that significant.
And yes engines were swapped out, not overhauled while the aircraft sat around idle. That is why I said that aircraft were doing some 2000 hours per year and engines up to 1500. Depending on the engine an operator would hold 30-100% spares for this reason (making my estimation of about 1500 way too high). Many operators did their own engine and component overhauls as depending on the manufacturer could result in your engines being held up in overhaul by brand X's engines so having your own shop guaranteed your engines got priority and were done the way you wanted.
Ten hours non stop for a DC-3 sounds like they were pushing the limit somewhat as my (very fallible) memory is that the DC-3 did not have that endurance. I will have to check.
EDIT - According to the USAAF C-47 flight manual the C-47 had an endurance of 11.82 hours if you made no allowances for take off and climb so that does make 10 hour flight possible but they would definitely be running on the smell of an oily rag on landing and have nothing in reserve. I suspect the earlier engines were a little less fuel efficient than the 1830-92 which would have shortened the range a little as well. I cannot find my DC-2 flight manual.
Most DC-3 were Cyclone powered, which were more fuel efficient than the Twin Wasp. In any event prewar models of both engines should have equal or slightly better fuel efficient do to less friction and lighter construction of moving parts. The typical DC-3 was a good 600-1500lbs lighter empty than a C-47 as well.
From the R4D-5 SAC sheet combat range for the R4D-3 was:
1295 n.mi./111kts @ 29000lbs
1405 n.mi./107kts @ 26000lbs
Both aircraft have the same fuel load of 4824lbs.
Cruising altitude was 1500ft. There is no breakdown of allowances if there are any. Because SAC sheets were designed as practical aides for mission planing, I suspect these range figures are most likely practical with allowances for
That 11.82 hours is based on the minimum specific fuel consumption rate 34 gph at 450hp. This is neither the minimum fuel consumption to maintain level flight nor the power for best range.