Which method? Categorical data (IV) and continuous numerical data (DV)

Thanks in advance for taking a look at my query

I have been trying to get some statistical support from my local research department but I am getting conflicting opinions on which statistical methods I should be using to analyse my data. Any thoughts or insights would be much appreciated.

I have health data which related to approximately 1000 individuals who have been designated to one of 6 groups, based on their pre-existing demographics, co-morbidities etc. (independent variable). Due to the way the groups are derived from real-world data the groups are of different sizes. The IV is therefore categorical data, which I could analyse using logistic regression by assigning the groups quantitative values.

The dependent variable is a measure of hospital length of stay in days, which is continuous data which has a positive skew in distribution towards shorter stays.

My hypothesis is that there is a relationship between the patient group ('young, healthy, independent', through to 'elderly, co-morbid, and dependent') and length of hospital stay, with healthier individuals going home more quickly.

I had begun to use a one-way ANOVA test to analyse this data which has yielded significant results and supported my hypothesis, however it has been suggested that other tests may be more appropriate.

I am keen to use the most appropriate test, even if this might disprove my hypothesis. Suggestions have included Kruskal-Wallis test, Mann-Whitney and Spearmans tests, although I have much less experience of these methods and am less familiar with their appropriate application.

Thanks in advance for your comments.