"How did you come up with this route?" For each of the (5 x 4 x 3 x 2 x 1) ^ 3 = 1728000 possible routes, I added up all the turns you'd have to make with the time machine's location and digits. This route is faster than every other route by at least two full turns.
"Have you considered the time it takes to walk from the door to the first artifact in museums 2 and 3?" Yes. It turns out running from the left artifact even to the far right one is faster than a turn. So even if there were a route that started museums 2 and 3 with the far left artifact and is only two turns slower than this route (which there isn't), it still wouldn't be faster than this route. In fact, there's only one route that's exactly two turns slower than this one that starts either museum to the left of this route (museum 2 starts with the third instead of the fourth artifact; obviously, this doesn't justify the two turn difference).
"Have you considered saving two A.D.-B.C. switches by ending museum 2 in Athens and starting museum 3 in Alexandria?" Yes. Switching from A.D. to B.C. or vice versa takes very little time, much less than a turn. There are no such routes that, even when combined with starting museum 2 closer to the left, would save anywhere near enough time to justify the turn difference.
"Have you considered any other considerations?" Air vs ground speed, exiting levels in the air, not having to move to the final digit(s). Nothing seems to make any other route faster than this one.
"Have you considered clipping and zipping and flipping and tripping?" No.
THE ROUTE
Start (Menlo Park, 1993)
Music (Up/Down 7 to Vienna, 1824, 12 turns)
Vienna 1770 piano Mozart deaf composer palace symphony 1824
Document (Up 1 to Philadelphia, 1776, 9 turns)
Thomas Jefferson Burgesses British voluntary speaker Independence 1776 President Monticello farmer
Apple (Down 5 to Cambridge, 1687, 8 turns)
Christmas Day Cambridge Black gravitation Motion astronomy spectrum reflecting 30 Principia
Book (Up 1 to Florence, 1505, 6 turns)
Vinci 1452 Renaissance Florence patrons architect Renaissance backward fresco Mona Lisa
Shield (Down 5 to Orleans, 1429, 12 turns)
Joan 3 English Saint Catherine 4000 Orleans Dauphin Charles VII heresy
Crown (Down 1 to London, 1595, 9 turns)
England Queen Elizabeth I Good Philip II Spanish Armada Queen of Scots confined treason Sir Francis Drake
Tile (Up/Down 7 to Gobi Desert, 1292, 13 turns)
Venice Niccolo Kublai Khan 17 3 Gobi Cambuluc Asia paper fireworks 1295 Persia Book 500
Scroll (Down 3 to Athens, 369 B.C., 11 turns)
Greece 387 B.C. university 900 Socratic Socrates Aristotle truth government 24 Republic meritocracy philosophers
Filament (Down 2 to Menlo Park, 1879, 9 turns)
Thomas Alva Edison Wizard gas Europe 200 filament bamboo light bulb alkaline patents 1000 perspiration
Flag (Down 4 to Calcutta, 1947, 10 turns)
Britain satyagraha 1915 1757 Mahatma death World War II Mountbatten passive
Staff (Up 1 to Alexandria, 47 B.C., 3 turns)
Egypt Ptolemy XII Alexandria Julius Caesar guardian coronation 47 B.C. Caesarion Marc Antony
G (Down 2 to Mainz, 1455, 10 turns)
Germany scribe read inherited print crooked 30 printing metal 1455 Bibles
Sextant (Down 3 to The Pacific, 1521, 11 turns)
India 1519 Spice eastern Tierra del Fuego 39 Pacific scurvy Del Cano globe oceans
Chisel (Down 2 to Florence, 1503, 6 turns)
Caprese 1475 stonecutters Ghirlandaio Lorenzo de' Medici David Sistine Chapel Julius II
Skull (Down 3 to Stratford, 1601, 6 turns)
playwright English play actor 37 histories tragedies Globe weather Stratford
Total: 135 turns + 4 A.D.-B.C. switches
At this point one might be tempted to start memorizing these lists of answers, or at least to have these in front of them while playing. I personally have a different method that I believe is faster, especially when the words are far down in the list of options. Instead of having a general sense of where the answer is alphabetically, I find it easier to instead look for the word that would be on the top of the display (i.e. the word that's eight places above the correct answer). Then you can time your A press with when that word reaches the top. Below is a list not of the answers, but of the words that need to be on the top of the list when you press A. Words in italics are on the first page, and they are preceded by a number that indicates how far down you'll need to go to reach the word on that page.
Music (Up/Down 7 to Vienna, 1824)
India 6 1770 English Joan astronomy 8 composer histories Republic 8 1824
Document (Up 1 to Philadelphia, 1776)
Philip II 6 Burgesses 3 British passive President fresco 7 1776 oceans Egypt Book
Apple (Down 5 to Cambridge, 1687)
7 Christmas Day 3 Cambridge 2 Black death guardian 2 astronomy Principia Globe 5 30 palace
Book (Up 1 to Florence, 1505)
Monticello 1 1452 patents Asia Independence 1 architect Good 1 backward composer Del Cano
Shield (Down 5 to Orleans, 1429)
7 Joan 4 3 Bibles Mona Lisa 8 4000 England 3 Dauphin 2 Charles VII farmer
Crown (Down 1 to London, 1595)
7 England Lorenzo de' Medici backward Julius II playwright Marc Antory 0 confined scribe Mountbatten
Tile (Up/Down 7 to Gobi Desert, 1292)
Greece Julius Caesar Charles VII 1 17 4 3 Cambridge 4 Cambuluc 1 Asia crooked Christmas Day 0 1295 Europe 5 Book 17
Scroll (Down 3 to Athens, 369 B.C.)
Cambuluc 1455 Spanish Armada 200 Pacific Mozart 0 Aristotle scurvy deaf 3 24 patrons gravitation Mahatma
Filament (Down 2 to Menlo Park, 1879)
Niccolo spectrum 7 gas 8 Europe 2 200 Burgesses 3 bamboo globe 0 alkaline History 0 1000 light bulb
Flag (Down 4 to Calcutta, 1947)
2 Britain perspiration 1452 5 1757 government bamboo stonecutters Ghirlandaio eastern
Staff (Up 1 to Alexandria, 47 B.C.)
6 Egypt Kublai Khan 0 Alexandria 8 Julius Caesar English architect 1475 1 Caesarion David
G (Down 2 to Mainz, 1455)
Britain philosophers 3 read 1 inherited 2 print 4 crooked 5 30 gas Black 2 1455 4 Bibles
Sextant (Down 3 to The Pacific, 1521)
Caprese 4 1519 paper 5 eastern Gobi 7 39 British play 5 Del Cano coronation heresy
Chisel (Down 2 to Florence, 1503)
5 Caprese 3 1475 Renaissance 6 Ghirlandaio Dauphin 4 David Florence Caesarion
Skull (Down 3 to Stratford, 1601)
Motion 6 English meritocracy 0 actor 6 37 filament satyagraha 8 Globe speaker Germany
Good luck!
