So are your custom URLs something like the Radio JRiver URLs? i.e. URLs pointing to specific tracks served from internet sites?
My custom URL collection is stored within Media Center playlists which have fields "Name" and "URL" (which is typically long and complicated) and one or two other things that I find useful but, I doubt are of real significance.
I think, based on your description, that if you copy the contents of your Custom [URL] field, which contains the URLs you want to play, to the [Filename] field, the URLs will then turn up in the Playlists and you will be able to play them. At least locally they will work. To copy the field contents, select the items in MC, then right-click on one and select "Library Tools > Move / Copy Fields" then complete the dialogue.
The question then really is whether MC will stream the URL media to your Roberts DLNA Renderer. Some streams can be sent by DLNA, some streams can't. I get very mixed results with that. So you will need to try it. Test with Radio Swiss Jazz to see how it should work, as I can stream that URL based media to a DLNA device without trouble.
For DLNA, set the Audio Mode to "Original" if that is what you want. "Options > Media Network > Add or configure DLNA servers > Audio > Mode". Radio Swiss Jazz also works with "Specified output format" when that format is supported by the DLNA Renderer. Try using L16 as that should always work, and then try other formats if you want once you have seen L16 work. You should probably set up a specific DLNA Server in MC for the Roberts radio, unless it is the only DLNA target device that you use.
If you have more than one DLNA Server in MC, you need to Associate the correct DLNA server with the Zone for the Roberts radio. Select the Zone under Playing Now, right-click it, select "Associate with DLNA Server", then select the correct Zone.
As for your Main Question, Playlists are Playlists. Their format and layout are well defined. You can display any fields as columns in a Playlist View, in the same way as any Views, but you can't change what a device is expecting in them, or what fields MC will look at when trying to play a Playlist. MC will look in the [Fielname] field for the target media. Hence the field copy recommendation above.
A simple third-party DLNA Server could easily send media to the Roberts radio, because it is simple and isn't as configurable or capable as MC. "With great power comes great responsibility", or something like that. Maybe "With greater functionality comes greater complexity".
If I have completely misunderstood your description, sorry, but I tried. Some of what you wrote doesn't make real sense in a MC context, such as "My custom URL collection is stored within Media Center playlists", because in MC your custom URLs would need to be created as items, possibly imported into MC initially, and then those items could be added to a Playlist. You can't directly create a Playlist in MC. Well, you can create the Playlist name, but it won't have any contents unless you actually add items to it.
Perhaps some screenshots of the items you have in MC for your custom URLs, and the Playlists they belong to would help.