Well OpenFietsMapsLite sounds as though it's derived more or less directly from OpenStreetMap. In which case the stock answer would be to go in and fix it yourself, because it's like a wiki. 'All' you need to do is create your OSM login, then learn a few of the basic drawing techniques and also the basic 'rules/etiquette' about what you should and shouldn't add. Then sit back and wait for your edits to propogate around until they appear in OpenFML. Be warned it's addictive.
Routing problems could be quite difficult to fix, because often there are a lot of dependencies going on, over quite a large area sometimes - 'fuzzy' decisions will have been made about road priorities and so on, fixing these can feel quite intrusive.
... this means 'punching a hole' in the Metroguide map around there...
ooh! How do you do that? Any specific editting software? Simple cut 'n' delete? 
Well no, just in the GPS itself, you can select an individual map tile and turn it off. (In setup map.) If you have another map underneath, it will then show through the resulting 'hole'.
Hmm - that's in my older Etrex - maybe you can't access the individual tiles in the E30.
But you can achieve the same thing by excluding a tile at the time of creating the map - for example in Mapsource you can select individual tiles and turn them on and off, before uploading to GPS - or in the Dutch routable OSM download site
http://garmin.openstreetmap.nl/ you can e.g. select a country and then tick 'manual tile selection' and de-select one or more tiles within that country, then download the result (takes longer to generate the file when it's non-standard like this).
[edit to add -] You can create two maps in this way - imagine a map of 81 tiles arranged like a Sudoku board - you could create one map of 79 tiles, all except 39 and 40 say, and another map of just 39 and 40. Load them both onto your E30. Both will appear in the Setup>Map menu, but very likely, both will have the same name. Doesn't matter, once you work out which is which. Having both enabled, you get a seamless map of the area. Disable the 39/40 map, and you punch a hole, through which another map could show. [end edit]
What may be more challenging is having some say in which maps occupy which levels. There are (I think) a possible 31 layers in the GPS, and of course any single map also has several layers built in, so that roads appear laid across woodland and not underneath, etc. AFAICS most Garmin detailed maps occupy layers between 25 and 30 (ie near the top). They are 'transparent' insofar as in areas where there is no mapping information at all, anything on a lower layer will show through. Any contours-only map should obviously go to layer 31 (and be set to be transparent). Garmin Worldmap (a crappy map that is better than the supplied basemap, but only just) occupies layer 5, I reckon. So there's lots of space in the teens for anything else, and I assume most of the online map generators allocate their maps to a layer in the 10-25 region. Without going deep, there is not much control over this.
