Hi
Hay mites (the are
not lice and the 'static' bit you see are actually the egg cases that are fixed to the hairs of the bum and the underlayer; there is only one variety of species specific lice) have got their current vernacular name because they come in the hay.
It is also
highly likely that the itching is from just the hay mites and not any resurgent mange mites so you are dealing with only one problem. Please accept that we can only ever comment on what you are telling us.
But the medical treatment for any skin parasites is the same so it won't matter in practical terms. By the treatment interval you have mentioned it is most likely vet grade xeno and what we also recommend on here.
Personally, I would strongly recommend that you radically cut off any hair that has eggs fixed to them and give your new arrival a really short haircut; go over the whole body and look beneath the top layer of hair. You will also have to check their companion. The mites could be from your or the rescue's hay; that is impossible to say for me.
It may not be sightly but that is going to get a whole lot of mites removed before they can emerge to multiply quickly and that you then need to treat chemically. This drastic but effective measure minimises the itching very quickly and helps to stop the hay mites in their tracks before they can really take off. The hair will grow back to its genetically determined length within a month. Unlike mange mites eggs in the skin, you can get at the hay mites eggs on the hairs, which makes it a lot easier to get a grip on them. You still need the ivermectin to kill any emerged hay mites that are around now or emerge from eggs you have missed but you can ensure that this is not going to be another major battle royale
Piggies from a really bad background can take a while to get their immune system up to full swing and their bodies totally recovered from their neglect/ordeal but once they do they can live just as long as normal piggies - I have had a fair number of them living to 6-8 years due to your good daily care which is the important bit; not rarely longer than piggies from a 'normal' background because deep down these piggies are true survivors. For me, it has always been more than worth any initial little wobbles.
More information on the various guinea pig specific parasites and the best way to deal with them:
New piggy problems: URI - ringworm - skin parasites