[As Coley - both of us having an early breakfast!]
Knotting is pretty economical. I still have half a bottle left over after doing the floorboards and 10" skirting in our bedroom.
You can also use aluminium primer, but in my experience it doesn't work quite as well (as knotting - otherwise an excellent primer) and it is quite expensive. It is very good for controlling mould and fungus though in damp situations, so I use it on skrtings (our place is old and fairly damp).
The proper stuff is particularly good for "dead" knots, the ones that have already started to shrink and which otherwise go loose over time. If you are in Bristol presently, Mogfords in WoT carry it in sensible-sized bottles for small jobs.
In this context, given the stock is probably barely better than horrible (I once bought some wood from Wickes!), I would use both, on both sides and the cut ends. Treat the knots themselves with knotting then two coats of Aly primer all over, especially the board ends, denibbing and flatting back between coats. That will make it as stable as you will probably get it, and stop anything coming through or falling out.
Flatting back the actual knotting can be a pain, especially if the wood is resinous - it's a mechanical barrier for the resin, and a thin glue for the dead knots. You are essentially removing it again by sanding. I don't know of a magic bullet - once you break through, the paper instantly clogs and smears, and you're almost at square one again.
Acetone or meths (or that thinner in tins from Lidl) seems to clean up the resin, bit it also dissolves the knotting! I've settled for a very slight ridge around the knotting patch (spread well past the actual knot), which can be feathered in with subsequent layers.
I know your finishing is excellent! The Aly primer can be annoying in that it shows through thin or patchy paint, but if it's to your usual standard there won't be a problem. And it does seal well if it's thick enough, so even in a bathroom things shouldn't move around too much.
E.
PS: if you are in Bristol and feel like a trip to Lidl today, TXT me - Southmead didn't get its tool delivery for yesterday, meaning going to one of the others :-(