You can use the functions imresize() or interp2() to rescale a matrix of 2D gridded data and calculate the sums in the output, if you multiply the result by the correct factor. This makes sense when you think of the output cells as containing the average value of the input cells. In order to convert the average to the sum, you have to multiply by the number of observations that were used to calculate the average.
Simple example:
% Create an 8 x 8 grid where every cell contains the value 1
A = ones(8);
sum(A, 'all')
% resize the matrix, making each dimension smaller by a factor of 4.
% Each cell in the output will be equivalent to 4 x 4 input cells, so scale up by a factor of 16.
A_upscaled = imresize(A, 1/4, 'bilinear') * 16;
sum(A_upscaled, 'all')
Example with data in the format of the original poster:
%% Create a grid with the same dimensions as OP, assign values using the famous peaks function
x = 0:1/5999:1;
y = 0:1/4529:1;
[X, Y] = meshgrid(x, y);
Z = peaks(X, Y);
% Plot the orginal grid and the new upscaled grid
figure
subplot(1, 2, 1)
imagesc(Z)
colorbar
title(sprintf("4530 x 6000 grid \n SUM = %e", sum(Z, "all") ))
% Resize the grid, and multiply all values by the square of the scale factor
scale_factor = 12.245;
Z2 = imresize(Z, 1/scale_factor, "bilinear") * scale_factor^2;
subplot(1, 2, 2);
imagesc(Z2)
colorbar;
title(sprintf("370 x 490 grid \n SUM = %e", sum(Z2, "all") ))
% The sums are approximately equal... errors due to floating point math and rounding
