If you don't need anything beyond the feature set of ECS and are happy to stick with AWS for the foreseeable future, then I'd advise you to listen to your gut - EKS is more complex, and needs a bit more looking after.

Personally, I'd disagree with your consultants on being able to avoid multiple AWS accounts as a selling point. When you need to isolate workloads or implement hard security boundaries, accounts are generally the simplest and most reliable way of doing that. Following the Well Architected Framework is a good standard practice and there are plenty of guides and examples to help you.

If things do change in the future, it's not actually that big a deal to deploy to EKS instead (or as well) - but for your needs, I think ECS would make a better starting point.

(And I agree with other posters that ECS Fargate is likely the best fit for you)