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You raise a lot of interesting issues. I'll give my thoughts on some of them. First, I think you're right that ""Eric"" is, at least in some sense, more readable. Second, you're right that we have article titles like Eric I of Norway and Eric VI of Sweden (but also Eirik II of Norway so it's not quite consistent). I think that a high level of Anglicization is expected for the names of royalty where familiar names tend to be used if at all available. If Eiríkr Hákonarson had ever called himself king I would be fine with having his article at ""Eric II of Norway"". But he wasn't quite royalty and he is a somewhat more obscure historical character than the kings so I'm not quite sure how to apply this. 

As for medieval usage I haven't made a complete study but what I've seen so far is that the Latin charters witnessed by Eiríkr during his life have ""Yric dux"" (most commonly) or ""Yrric dux"" or ""Iric dux"". The Encomium Emmae, written in Latin in 1041 or 1042, has the form ""Eric"" and titles him as ""dux et princeps provintiae quae Nordwega dicitur"".

The Anglo-Saxon chronicle (written in Old English, of course) has ""Irke"" (a dative form) or ""Yric"" or ""Yrice"" (a dative form) or ""Eiric"". (Maybe I missed a variant.)

Old Norse texts are usually published in normalized orthography where the name is ""Eiríkr"". In diplomatic editions you will probably find forms like ""Eirikr"" or ""Eiricr"" or ""Eirijkr"" but I don't have any at hand at the moment so don't take it as gospel.

I've got to run now, will address the rest of the question later. I'm actually more worried about the patronym )  "