Hello Mark,
Please copy and paste this code. It should fix all your issues 
Suggestion: replace white, red and blue with true Hexadecimal color coldes:
ex: "background: #FFF" instead of "background: white" 
.rscrosstab .sapzencrosstab-HeaderCellDefault, .sapzencrosstab-DataCellAlternating
{background-color: white !important; }
.rscrosstab .sapzencrosstab-HoverRowHeaderCell.sapzencrosstab-HeaderCellDefault {background: red !important;}
.rscrosstab .sapzencrosstab-RowHeaderArea .sapzencrosstab-HoverRowHeaderCell.sapzencrosstab-HeaderCellDefault
{background: red !important;}
.rscrosstab .sapzencrosstab-RowHeaderArea .sapzencrosstab-HoverRowHeaderCell.sapzencrosstab-HeaderCellAlternating
{background: red !important;}
.rscrosstab .sapzencrosstab-DataArea .sapzencrosstab-HoverDataCell.sapzencrosstab-DataCellDefault
{background: red !important;}
.rscrosstab .sapzencrosstab-DataArea .sapzencrosstab-HoverDataCell.sapzencrosstab-DataCellAlternating
{background: red !important;}
.rscrosstab .sapzencrosstab-RowHeaderArea .sapzencrosstab-SelectRowHeaderCell.sapzencrosstab-HeaderCellDefault
{background: rgb(203, 204, 204) !important;}
.rscrosstab .sapzencrosstab-RowHeaderArea
{background: rgb(203, 204, 204) !important;}
.rscrosstab .sapzencrosstab-DataArea .sapzencrosstab-SelectDataCell.sapzencrosstab-DataCellDefault
{background: rgb(203, 204, 204) !important;}
.rscrosstab .sapzencrosstab-DataArea .sapzencrosstab-SelectDataCell.sapzencrosstab-DataCellAlternating
{background: rgb(203, 204, 204) !important;}
.rscrosstab .sapzencrosstab-HeaderCellHoverRow
{background: red !important;}
.rscrosstab .sapzencrosstab-HeaderCellSelectRow
{background: blue none repeat scroll 0% 0% !important;}
.rscrosstab .sapzencrosstab-DataCellSelectData, .sapzencrosstab-DataCellAlternating.sapzencrosstab-DataCellSelectData
{background: blue none repeat scroll 0% 0% !important;}
regards,
Bogdan