All my googlefu finds is that in 1939 the female labor participation rate was still at 37%.
Well, my googlefu says that the female labour participation rate did indeed rise from 1937 to 1939... by 2%, to 33%. Oh well.
German production almost doubled from '33 to '37 and military spending increases only accounted for a fraction of that increase. That is a very, very rapid increase in non-military economic activity. Even if a railways eventual purpose is military activity in 1940, it can still be used for civilian activity in 1937 and it's construction still puts money in the pockets of working men in 1936.
True, a lot of the gearing up for war consisted of infrastructure spending, but in real terms, it was pretty close to useless infrastructure spending. It didn't help the German government simply due to design incompetence; for example, many new German roads were created for the purpose of allowing fast transportation of Wehrmacht forces (tanks and heavy artillery in particular) from one front to another, yet it was discovered that they couldn't bear the weight of armoured columns, which had to use older modes of transportation anyway. Further, they shined so brightly (they were painted white) that they made easy targets for Allied bombers.
For civilians, the new infrastructure had its uses, but it certainly didn't promote economic activity since, to all intents and purposes, Germany had a planned economy at the time. Actual economic decisions were largely made by high officials in the Nazi party, with limited decision making being granted to betriebsführers, the former capitalists. Any economic benefit of the new infrastructure went almost entirely to the German state (and that benefit wasn't necessarily great either, see above). And again, if you want to compare planned economies, the Soviet Union was simply more efficient than Nazi Germany in raw production despite many disadvantages, yet even those that say Hitler's stimulus was successful wouldn't support simple nationalization of the entire economy.
I am unaware of rationing in Germany before the war started in 1939. There would of course be material shortages but that's just because of a lower total productivity factor and capital accumulation compared to the standard we in the US are used to. The per capita gdp of 1930s germany was about 1/6 of todays, putting them a little below where Ukraine or Georgia is today even before you account for that military spending. At that level of per capita gdp, shortages happen. Unless you can show that shortages were worse in 1937 or so compared to 1929 or 1928, the existence of shortages doesn't really tell us much. Unless the economy gets derailed first, people in 2080 will talk about the shortages of consumer goods that plagued the US in the year 2014.
German economic shortages and rationing existed even relative to the standards of the time. Even a German living prior to WW1 would be in better shape economically than one living in the 1930s. So far as evidence goes, well,
here you go (warning: LONG). I suppose Richard Evans is a Marxist so you might consider him biased, but his analysis is worthwhile.