There is a great introduction to the pitfalls of categorizing continuous variables on this page, with links to more information. It seems that you have a continuous predictor that was linearly related to log-hazard with no (or some simple) transformation, so you should take advantage of that simplicity as much as possible. Even in practical terms, once you got to a 3-level ordinal categorization you were using up more degrees of freedom than you did with the continuous representation.
In terms of displaying results, you could do the statistical analysis with the continuous analysis and illustrate with Kaplan-Meier plots based on binning of the predictor values. With multiple covariates affecting outcome even that type of display is potentially misleading, as the plots hide the associations of the other covariates (and their own relationships with outcome) with your predictor of interest. There's no assurance that empirical Kaplan-Meier curves will properly represent the relationship between your predictor of interest and outcome (although a reviewer might well want to see them).
Perhaps a better choice would be to plot predicted survival curves, with confidence intervals, based on the Cox model. If there is a set of covariate values that is consistent with a reasonable range of your predictor of interest, you could set the other covariates to that set of values and show predicted survival curves for 3 or so values of your predictor of interest that span that range.