NavList:

Gary, sadly I have found those IKEA tapes to lack quite a bit in accuracy, on the other hand I amtrained to deal with at best micro meters in the teens as tolerance (0.013mm is just above half a thousandth of an inch).

Lu, get Dr kolbes Almanac instead, much more compact and about as accurate, only thing that makes it less than NA is the lack of moon and planets.
considering the work needed to calculate those accurately even using calculator... not practical for long term almanac use.
one could use sun/star distance if one had transit and steady ground to get decent "solar" (as oposed to lunar).
no tools, papers...
My bet would be making a nocturnal using my earlier 57.296 solution, just, remember the ofset betweeen line from E-cassiopeia, kochab and dubhe to polaris and actual pole, then the 42' away from perfect 90°declination that should get you to ±20min of actual time, not GPS but built from nothing it is about only way I can think of to get longitude this side of full blown lunar.

miracle? uhm,
how about telling the local blacksmith how to make shearsteel, considering that at the time iron was close to silver in price and good sword steel MUCH higher...
making a decent running pendulum clock.
making a compass
making a spark transmitter (powered by a salt-water or vinegar battery) and crystal receiver and use the combo to send a message few miles across a lake or field, these will require quite a bit of thin metal wire and sheet metal, not impossible amounts.

sadly burning at stake is likely outcome of most above (not first I think) if I have not managed to persuade local lord that the tactical/strategic benefit of good "invisible" signalling is a god-sent gift to give the righteous lord the advantage in battle)
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