Heatmap of read coverage around TSSs

I am trying to plot a heatmap of read density around a feature of interest (TSSs) very common in genomics papers. something like this (B):

However, I am struggling a bit in getting to look "right". A bit of background: I have mapped ChIP-seq reads for pol2 and calculate the coverage, per nucleotide, using bedtools.

coverageBed -d -abam $bamFile -b $TSSs > $coverage.bed
# output:
chr1    67108226    67110226    uc001dct.3    16    +    1    10
chr1    67108226    67110226    uc001dct.3    16    +    2    10
chr1    67108226    67110226    uc001dct.3    16    +    3    10
chr1    67108226    67110226    uc001dct.3    16    +    4    10
chr1    67108226    67110226    uc001dct.3    16    +    5    8
chr1    67108226    67110226    uc001dct.3    16    +    6    8
chr1    67108226    67110226    uc001dct.3    16    +    7    8
chr1    67108226    67110226    uc001dct.3    16    +    8    8
chr1    67108226    67110226    uc001dct.3    16    +    9    8
chr1    67108226    67110226    uc001dct.3    16    +    10    8

Then in R, the genomic position, in column 7, is converted to relative position to the TSS and read counts normalized to the library size. This is converted to a numeric matrix with each row being a TSS and each column the relative nucleotide position. For the plotting the matrix is ordered number of reads per TSS, and the values logged. This is the outcome:

heatmap(cov.mlog, Rowv=NA, Colv=NA, scale="column", labCol = FALSE, labRow = FALSE, col=brewer.pal(9, "Greens"), margins = c(5, 5))

Although the average coverage plot looks as one would expect for pol2, the heatmap is, well, not great. My question is what am I doing wrong and how to improve it? In this and this paper, the coverage is calculate for a bin of nucleotides and not per nucleotide as I am doing. Would that improve visualization? How to do it in bedtools? Should the sorting of the matrix be done differently?

I am aware that could use ngsplot for this, but I am trying to avoid it because my implementation would fit better with my other analysis.

Thank you!