Hi Jonathan,

Might be easier to work with Quantity rather than TimeObject.

(* Convert TimeObject to Quantity *)
times = Quantity[MixedMagnitude[#], MixedUnit[{"Minutes", "Seconds"}]] & @@@ timestamps

(* Convert to seconds *)
seconds = UnitConvert[#, "Seconds"] & /@ times

pointList1 = Thread[{seconds, measurements1}];
pointList2 = Thread[{seconds, measurements2}];

DateListPlot[{pointList1, pointList2}, PlotLegends -> {"first run, slot 3", "second run, slot 3"}]

lm2 = LinearModelFit[QuantityMagnitude /@ pointList2, x, x]

Show[DateListPlot[{pointList1, pointList2}, PlotLegends -> {"first run, slot 3", "second run, slot 3"}],
 Plot[lm2[x], {x, 54, 1500}, PlotStyle -> Blue]]