This question has been answered by yasya_popkin. See the first response.
Specify the context in the snippet properties - &contexts=`web`. Make sure the 'web' context Context Settings are set for the site_url and base_url.getResources make links, related to web context, even if user located in other one.
{"published":"1","deleted":"0","context_key":"SomeContextName"}maybe, you would be better, to have all this projects in a custom table?No problem, I can. But I don't believe that there are no any solutions for MODX.
[[~[[+id]]? &scheme=`full`]]