Combine two DateListPlots and retain a time axis

I am trying to combine two DateListPlots to produce a single chart with 2 y-axis. There is an example here with regular Plots and I have tried to adapt it for time based data https://reference.wolfram.com/mathematica/howto/GeneratePlotsWithTwoVerticalScales.html

The code below creates smallMeasurements and bigMeasurements, plots each on its own graph, rescales one so they can be seen on the same chart, and then combines them.

The problem I cannot fix is that on combining the charts the X-Axis no longer displays time. Does anyone know some magic to fix this?

timesSteps = Map[Function[AbsoluteTime[{2014, 1, 1, 9, #, 0}]], Range[0, 480, 10]];
values = 1 + N[Sin[2*Pi *Mod[timesSteps/60, 360]/360]];

smallMeasurements = ArrayReshape[Riffle[timesSteps, values], {Length[values], 2}];
bigMeasurements = ArrayReshape[Riffle[timesSteps, 1000*(2 - values)], {Length[values], 2}];

smallPlot = DateListPlot[smallMeasurements]
bigPlot = DateListPlot[bigMeasurements];

smallRange = ReplaceAll[PlotRange, AbsoluteOptions[smallPlot, PlotRange]][];
bigRange = ReplaceAll[PlotRange, AbsoluteOptions[bigPlot, PlotRange]][];

leftTicks = N[FindDivisions[smallRange, 5]];
rightTicks = Quiet[Transpose[{leftTicks, Map[Function[ToString[NumberForm[#, 2], StandardForm]], Rescale[leftTicks, smallRange, bigRange]]}]] ;

bigPlotRescaled = ReplaceAll[bigPlot, Graphics[graph_, s___] -> Graphics[GeometricTransformation[graph, RescalingTransform[{{0, 1}, bigRange}, {{0, 1}, smallRange}]], s]]

Show[smallPlot, bigPlotRescaled, Axes -> False, Frame -> True,
FrameStyle -> {ColorData /@ {1, 2}, {Automatic, Automatic}},
FrameTicks -> {{leftTicks, rightTicks}, {Automatic, Automatic}}]   