The main point is that it´s not a good idea to try to climb Hekla.
If you are experienced in the use of ice axe and crampons, it is perfectly plausible. Tours for suitably fit tourists are arranged, though they have a fairly high failure rate because of the weather. I think it is best to understand the real reasons for doing or not doing things. Eruption risk is not the reason: eruptions generally have forewarning.
not Reykjavik
I was just explaining which Borgarfjordur was likely meant in the itinerary OP himself presented, in order he could understand it. It is perfectly plausible to include Borgarnes area in a south coast tour if you have time, the traveller will pass through Reykjavik and it is less than an hour away; there are connecting roads without returning to R. OP can decide for himself whether he has enough time according to his own style of travelling.
