Disclaimer - I am not an expert but this is what I do.

Your Ben Sarek is a black currant, Ribes nigrum. I find the easiest way to prune these is to do it as you harvest. Just cut off the whole branch with the fruit on it right at its base. Find a comfortable seat and strip the fruit off. Dispose of the branch. (You could use them as cuttings. Stick them in the ground and I defy you to stop them growing. That's your black currant pruned.

Your red currants are Ribes spp. (rubrum or sativum). These can be left alone if you wish. Otherwise you can just remove old or crowded wood when it looks necessary. That's why you can grow them as cordons or espaliers because you can build up a permanent framework of branches. They are almost as easy as black currants to grow from cuttings.

I emphasise that this is just my lazy, err.. I mean time-efficient, way of dealing with them. For more detail on doing them the experts' way Google or find a book.

Your "unsophisticated" method of pruning works really well for me,too, in central Ontario,Canada .....I get a quart or two from each of my red currant bushes.
And I think you have very sensible priorities, about which fruits deserve lots of time & effort.....& which ones don't really need it.My compliments to you ,for not recommending the complicated training that the "experts" believe is necessary.
On my red currants, each year , I just cut out 1 or 2 of the OLDEST,gnarliest,most lichen-covered canes.... never more 2 canes, unless they're damaged.
I've noticed that the 4 & 5 year old canes,on my red currants, produce less than the slightly younger canes & it seems to encourage new canes,by cutting out the oldest 1 or 2 .....I guess this is basically the same as what you're practicing??)

I have other black currants, not the type you have. I actually wanted a much taller variety (6 ft tall). So I don't think I can give you a suggestion there. In my case, I thin my bushes out 25% every late winter.

But for red currants: I cut out a few (I would suggest 25%) old branches to the ground every year (February) and let the new shoots come up from the ground. Those new shoots will have fruit the following year as well as the old shoots will still have berries for a couple more years.

I find currants very easy maintenance.