I think you are really asking an iPad question, more than an Exchange ActiveSync question.
In iPad Settings > General > Guided Access, you can enable a "kiosk mode". Apple just calls it Guided Access, but what you're effectively doing is locking the tablet to a single application. With the feature turned on, triple click the Home button to lock the application. You can configure a PIN to release Guided Access, or rely on the obscurity of the triple click to unlock the device.
As for ActiveSync, you should create a new ActiveSync policy and assign it to the room mailboxes. Normally a room mailbox account is disabled, but I would imagine your solution gets around that issue.
Creating a new policy can be accomplished in the Office 365 Exchange Admin Center, under Mobile > Mobile Device Mailbox Policies. Click the Plus [+] to create a new policy, give it a name, and configure options. I would advise against not requiring a password. You can leave the "Require sign-in after the device has been inactive for X minutes" option, and I think that will allow you to set the auto-lock to Never.
Finally, I suggest you audit usage of this ActiveSync policy, since it is less restrictive than normal.
You can also create and modify ActiveSync policies using Powershell, using New/Get/Set-MobileDeviceMailboxPolicy. Get and Set-MobileDeviceMailboxPolicy is going to be useful for enumerating some of the more obscure settings and requirements, you might find something useful.