Lou, -you are a little late for unsupported crossing of Iceland. You are crossing an inhabited land with farms, roads, bridges, weather service, SAR and mobile phone coverage. Assistance is only a phone call away and can be expected in a few hours. There is no “self reliance” when ambulance and hospital is only one phone call away, -just like the hike from London to Birmingham.
There is nothing extreme about ploughing from one side to another and not using kites is to us some strange British masochism and has resemblance with Scotts attitude against skis.
Crossing Iceland from one corner to another is old news and has been done countless times in all seasons except the dead of winter (late Nov to mid Feb). April and sometimes May are winter months. The question is who is doing this in the best style, – speed (kites) most interesting route and above all, -who is having the most fun.
The locals are mostly interested in the highland and glaciers. Rambling between farms and sheep pastures in the lowlands is more like shopping for groceries.
This winter crossing from 1916 is truly remarkable but according to you criteria it was supported as Sturla was accompanied by a friend on day one.
http://timarit.is/view_page_init.jsp?pageId=999047