I had a look at this but only saw one reference that was anything like what you asked for:
Bossi, P., Antonuzzo, A., Cherny, N. I., Rosengarten, O., Pernot, S., Trippa, F., ... & Ripamonti, C. I. (2018). Diarrhoea in adult cancer patients: ESMO Clinical Practice Guidelines. Annals of Oncology.
Article Diarrhoea in adult cancer patients: ESMO Clinical Practice Guidelines
The authors did not feel that there was enough evidence for oncological patients with diarrhoea but that more research was needed. It might be worth contacting those on RG about any further work that they are aware of.
You can look at this other way around. A high FODMAP diet induces in a large quantity of patients GI complaints. Introducing a low FODMAP diet will therefore probably also ameliorate GI complaints in a oncological setting. However, we shouldn't expect a reduction in inflammation/mucositis itself. Similar findings have recently been reproduced in an IBD setting (sept 2019 Gastroenterology). I would however think twice about introducing such a strict diet in a generally suboptimally fed population.