I agree that the described, smaller message is Site Settings makes sense. I've created a mock to show how I understand it.
I've been thinking where to place the UI, whether to site administration itself, or the template administration. Both locations make sense to me, but template one a little bit more.
(1) Instead of just forced propagation, I'd reset the counter and then invoke a regular merge using com.liferay.portlet.sites.util.SitesUtil.mergeLayoutSetProtypeLayouts() resp. com.liferay.portlet.sites.util.SitesUtil.mergeLayoutProtypeLayout(). Those methods have so much code around the actual merge (timestamps, fail counter, locking etc.) The the code in those methods would need to be refactored and new method created, which would do just the merge and throw exception in case of any error. Then we would propagate this exception to the user (site admin, who invoked Reset & Merge).
(2) In case of Site Template, when site was changed, template is not applied any more, but Site Settings portlet does not indicate this (in comparison to Dockbar on the site, where you see the message of stopped propagation). Should the new warning message and Reset & Merge somehow reflect this (not being avaialble, or only with confirmation)?
(3) Should I change the UI in Site Templates portlet and Page Templates portlets to be the same, smaller, as in Site Settings? I can imagine the counter being hidden, till the threshold is met. Then small warning saying "Propagation Disabled Temporarily" will show up, being a link to similar pop-up as in Site Settings. The forced merge here may be a little problematic, since there may be many sites linking the template. Should the template be pushed to all linked sites? I'd prefer to leave just the counter Reset here, then the template will be merged lazily. Also as said in #2, some site my be linked but changed, making the link inactive, so forced push of template should be up to the site admin, not the template admin.
Thanks for your thoughts,