By the new simplified web app I assume you're refering to the new Meetings App. I use the new meetings app in place of the previous skype for business web app without any problems - so I'm afraid I haven't experienced the same issue. As you probably know, there's no dependancy on the FE servers when using it other than the redirect to the Microsoft CDN, so it's perhaps worth testing on a non-domain joined machine, resetting IE to default settings, different user etc.... there must be a querky browser related restriction in play somewhere.
