Yes I knew about drawing lines on a My Map; the interface to do is quite awkward to use, but only straight segments and AFAIK there's no way to set color or line width or dash/dot. In other words, it is like so much about Google Maps: it is infuriating because it teases you with what it could be but is not.
Thank you very much, however, for leading me to what I couldn't find before, the iframe embed code for a "my map". It isn't anywhere under "Share" of course; it's hidden under the folder icon.
...the layer menu fills 1/3 of the iframe and won't go away. Another demonstration of GMaps teasing you with function that is almost helpful but not.
Here's another: in My Maps you can create a layer that includes directions from A to B for car, bike or walking, but you cannot show directions using the public transit mode. Why? What tourist does not want to show a route that involved a train or bus?
Yet another: when you create a layer with directions, it does not support directions to/from any of the points you've defined on that or another layer. Each destination has to be a new search.
Anyway excuse the anti-GMaps rant; my point is that this an application that would have wide use by many, the underlying engine (Maps API) is there, a clean, well-thought-out UI based on that engine could be a winner.
They're embeddable on websites too - https://support.google.com/mapsenginelite/answer/3024935?hl=... (although with low limits on the number of views)
http://milermeter.com (used to be http://gmap-pedometer.com) also lets you draw on maps but I'm not sure how embeddable they are.
You could export the GPX from miler meter into GPS Visualizer and use their "share my map" feature - http://www.gpsvisualizer.com/atlas.html
Faffy though, you're right.