Passing a custom variable from preprocess view to a template file
I'm not fully sure what I'm going to tell you is completely true, it is just my experience of how Views works.

From what I know, Every preprocess function has access to a specific output template file. As an example variables of template_preprocess_views_view_fields are available in views-view-fields--AnyThingElse.tpl.php template file, so the domain access of variables of template_preprocess_views_view_fields is views-view-fields--AnyThingElse.tpl.php.

In Theme Information there are three levels of output styles:


Display output
Style output
Row style output


The views-view-list--mycustomviewname--block_1.tpl.php is a TPL file in the second level (Style output) but I guess the mycustomtheme_preprocess_views_view domain of access of its variables is in the first level (Display output) TPL files.

To make sure, select one of the TPL files from Display output and check if the variable is set in there.