Sync[log_String, f_] := (
tlog=ToExpression[StringReplace[
log, {"[" -> "{", "]" -> "}"}
]];
tlog[[1]] = 0;
Do[
tlog[[i,1]] = Round[f[tlog[[i,1]]]],
{i, 2, Length[tlog]}
];
StringReplace[
StringReplace[
ToString[tlog, InputForm],
{"{" -> "[", "}" -> "]"}
],
"\"]," -> "\"],\n"
]
)

oldlog="log=[1297627474920,
  [253964, [1,1], \"Handout view 2: Abstract 1\"],
  [444894, [1,2], \"Handout view 3: Abstract 2\"],
  [613813, [1,3], \"Handout view 4: NCGE Handout\"],
  [757772, [1,3], \"Handout view 4: NCGE Handout\"],
  [788259, [1,4], \"Handout view 5: The Problem\"],
  [799050, [1,5], \"Handout view 6: A Demo Program\"],
  [810339, [1,6], \"Handout view 7: The Rubik's Cube\"],
  [820209, [1,7], \"Handout view 8: The Answer\"],
  [835128, [1,8], \"Handout view 9: Homework Problem 1\"],
  [855314, [1,5], \"Handout view 6: A Demo Program\"],
  [857391, [1,4], \"Handout view 5: The Problem\"],
  [862368, [1,6], \"Handout view 7: The Rubik's Cube\"],
  [864830, [1,7], \"Handout view 8: The Answer\"],
  [867078, [1,8], \"Handout view 9: Homework Problem 1\"],
  [887797, [1,7], \"Handout view 8: The Answer\"],
  [891164, [1,6], \"Handout view 7: The Rubik's Cube\"],
  [899380, [1,7], \"Handout view 8: The Answer\"],
  [906500, [1,8], \"Handout view 9: Homework Problem 1\"],
  [928003, [1,9], \"Handout view 10: I could be a mathematician\"],
  [939714, [1,10], \"Handout view 11: or an art historian ...\"],
  [948073, [1,11], \"Handout view 12: Left Eye\"],
  [953310, [1,12], \"Handout view 13: Right Eye\"],
  [966742, [1,13], \"Handout view 14: or and environmentalist ...\"],
  [981993, [1,14], \"Handout view 15: CO2 Emissions\"],
  [1003998, [1,15], \"Handout view 16: Smokestacks here\"],
  [1011454, [1,16], \"Handout view 17: Distress penguins here\"],
  [1017872, [1,15], \"Handout view 16: Smokestacks here\"],
  [1020781, [1,16], \"Handout view 17: Distress penguins here\"],
  [1028286, [1,17], \"Handout view 18: Goal\"],
  [1036949, [1,18], \"Handout view 19: Speed limits above the Mona plane\"],
  [1300301, [1,19], \"Handout view 20: Fermat's Principle\"],
  [1466477, [1,20], \"Handout view 21: The Brachistochrone\"],
  [1702318, [1,21], \"Handout view 22: Airline Route Maps\"],
  [1850063, [1,22], \"Handout view 23: The Least Action Principle\"],
  [1911242, [1,23], \"Handout view 24: The Sphere and the Pseudosphere\"],
  [2098888, [1,24], \"Handout view 25: The Happy Segway Principle\"],
  [2364337, [1,25], \"Handout view 26: Segways above the Mona plane.\"],
  [2448700, [1,24], \"Handout view 25: The Happy Segway Principle\"],
  [2459811, [1,25], \"Handout view 26: Segways above the Mona plane.\"],
  [2555806, [1,26], \"Handout view 27: The Lobachevsky Plane\"],
  [2558357, [1,25], \"Handout view 26: Segways above the Mona plane.\"],
  [2940056, [1,26], \"Handout view 27: The Lobachevsky Plane\"],
  [3242734, [1,27], \"Handout view 28: Lobachevsky\"],
  [3254471, [1,28], \"Handout view 29: Life in the Lobachevsky Plane\"],
  [3455370, [1,29], \"Handout view 30: Finding the Centre\"],
  [3496918, [1,30], \"Handout view 31: Parametrization\"],
  [3555189, [1,31], \"Handout view 32: The Actual Code\"],
  [3598014, [1,32], \"Handout view 33: Ops used\"],
  [3616474, [1,33], \"Handout view 34: We had a goal...\"],
  [3619689, [1,32], \"Handout view 33: Ops used\"],
  [3624305, [1,33], \"Handout view 34: We had a goal...\"],
  [3634424, [1,34], \"Handout view 35: we attained it...\"],
  [3639295, [1,35], \"Handout view 36: we used all keys ...\"],
  [3644503, [1,36], \"Handout view 37: The Hardest Math I've Ever Really Used\"],
  [3649959, [1,37], \"Handout view 38: is related to Lobachevsky\"],
  [3656592, [1,0], \"Handout view 1: All\"],
  [4029815, [1,23], \"Handout view 24: The Sphere and the Pseudosphere\"],
  [4121166, [1,23], \"Handout view 24: The Sphere and the Pseudosphere\"],
  [4211209, [1,20], \"Handout view 21: The Brachistochrone\"],
  [4517568, [1,22], \"Handout view 23: The Least Action Principle\"],
  [4563099, [1,20], \"Handout view 21: The Brachistochrone\"],
  [4761178, [1,22], \"Handout view 23: The Least Action Principle\"]
]";

pairs = {
{253964, 0},
{444894, 1000(3*60+8)},
{3656592,1000(56*60+40)},
{4029815,  1000(3600+2*60+43)},
{4517568,  1000(3600+10*60+50)}
}

Sync[oldlog, Interpolation[pairs, InterpolationOrder -> 1]]