On the former example, even if you see your way through to 6000ft you are then likely going to enter IMC from there up to 8000ft when you reach 0C. Then you continue IMC up to perhaps 10000-11000ft , but cloud cover seems partial up there.
So the tricky part is 8000-10000 or 11000ft. That is going to be 3-5 mins in normal climb on our airplane, but that is very type-dependant. Again I would not do a normal climb but one at high IAS which may take a bit longer, then change climb mode if icing is found. Also VMC is expected ahead as confirmed by the staellite pic for that time
Last, if you ice up you can always descend over the sea into positive temps.
IN summary, I would not see it such a big issue in this case, other than: how to stay away from CB in the IMC part? Since cloud cover is low, I might feel comfortable using radar and lighning just prior to departure and GOLZE in flight. Inflight WXradar and stormscope even better but not essential, since in any case we are talking of only the first 15 mins of flight.
As to the second case, I would only feel safe flying low level for the first 80nm and only then climbing. Otherwise it is a long climb in IMC, potential icing (although not forecast by GRAMET) and the need to navigate ISOL embedded CB’s. Too many cons…With deicing, radar and a lot of power…perhaps
Yes; I would not climb into such a convective mass.
Well, not unless somebody would set off a nuke behind me 
and then the TKS ought to do the job for long enough.
I would depart low level, underneath it. The 0C level is plenty high enough so no risk of FZRN even if you were in IMC. And much of the flight is over water so you can go “low”.
OTOH the actual wx might be very different. The gramet is often inaccurate in its depiction of clouds. They are generated from generic rules applied to the GFS model.
