Hi Teresa,
I suggest that you go into it with a couple of options in mind. One option: you love the experience, you decide that it's going to be really important to you to finish the full walk on foot, and thus you walk as far as you can and then plan to return to that spot next time (maybe this means Gijón or Oviedo, or maybe a shorter walk to Villaviciosa--you'll have transport options from all three, but certainly more from the first two). Another option: you like the experience, but don't think returning to the Camino will be a major priority over the next few years (or ever). In that case, perhaps it's worth the push to Santiago, just to get the experience of arrival. The big question will be which route to pursue--there's no reason it has to be the Norte. Given where you'll be coming from, I'd suggest considering taking a train to Lugo and then walking from there on the Primitivo/Francés.
Keep in mind that the transportation portion of this might consume more time than you anticipate right now, and that you might not enjoy packing too much into a limited timespan. For example, is it worth sprinting into Santiago if you don't have any time to enjoy it afterward? I'm not sure what your whole timeline is--just operating from the 3-4 day estimate.
No need to commit to either ahead of time, so it's probably best to act based on how you're feeling after the initial stretch of walking concludes.
Hope you have a great experience!