This does not completely resolve your problem, but it may be helpful to get you started:
% Load your data
all_data = load('struct.mat');
all_data = all_data.struct;
lat = all_data.lat;
mlt = all_data.mlt;
heat = all_data.heat;
% Plot your data in polar coordinates instead of geographic axes (because I
% do not think geographic axes support MLT)
figure(1)
polarscatter(mlt,lat,40,heat,"filled",'s',...
'MarkerFaceAlpha',0.6,...
'MarkerEdgeAlpha',0.01)
colormap('parula')
caxis([0 40000])
cb=colorbar;
thetaticklabels(cellstr(string(linspace(0,22,12))+"MLT")) % Change the "longitude" labels to MLT
pax=gca;
pax.RDir="reverse"; % Flip the inner tick marks so that 90 degrees South is at the origin
pax.RTickLabel = []; % Remove the inner tick labels
% Import coastline data for drawing Antarctica
load coastlines
% Find the index positions for Antartica in the coastline data sets
idx_180 = [find(-180 == coastlon,1,'first'),...
find(180 == coastlon,1,'first')];
% Extract the coordinates for the Antaractica coastline
polar_lon = coastlon(idx_180(1):idx_180(2));
polar_lat = coastlat(idx_180(1):idx_180(2));
% Add Antarctic coastline to the polar projection
hold on
pplt=polarplot(deg2rad(normalize(polar_lon,'Range',[0 360])),...
-polar_lat,'.'); % "longitude" must be in radians, and I normalized
% the data from 0 to 360 because otherwise the range is -180 to 180,
% which is not the degrees of a circle
pplt.Color = 'w';
hold off
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The issue with what I've done above is that I do not know how magnetic local time works, so the label positions for 0MLT through 22MLT may not be where you expect them to be. Additionally, I am not certain whether the size of Antarctica is scaled correctly relative to your data. You may have to normalize polar_lat to a different range.
Hopefully you find this helpful.
