Hi Lower, thanks for your suggestions which zero in on what I think I'm going to do.
Good call on bulking out the notch prior to resin, I'll have to see whether that stuff can be bought in smaller quantities. Not calculated the exact volume but it's not far short of a litre which is the mimimum pack size. There's also products like epoxy in putty form which would probably be as good. None of it cheap though
I don't have the luxury of sistering both sides as plumbing gets in the way of a good run at the back of the joist, so I would apply decent reinforcement to one side only, planning the arrangement so that it could be augmented in the future when the plumbing is replaced (No point replacing pipework until new boiler install which in turn has to wait until 'wallet deflection' is sorted out...)
I have some 25mm ply (extremely stiff), which I'll use to sandwich a piece of 3mm steel checker-plate against the joist, all mating faces bonded with structural adhesive and all fastened through joist with M10 Coach bolts, using M10 coach screws where rear access is out (screws and bolt positions staggered with alternating wood screws filling out the grid say No.10 x2½ ) All drilled holes to provide a snug fit on the shanks of the screws and bolts, any play would defeat the point of the object.
Pictures describe it a lot clearer.
Total run of reinforcement, 600mm either side of the notch. Depth to match joist depth with a small clearance at the bottom for plaster.
I suspect that although only 28mm thick in total, the lamination will at least match and hopefully exceed the stiffness of a single thick piece of timber, and being relatively thin have the advantage of being more easily manoeuvred into the floor void ripping the bare minimum of floorboards which, as you say, are helping the situation a lot.
Replacing a lifted floorboard which spans the two neighbouring joists is not as straightforward as it sounds: unfortunately the boards to the rear are pinned down by the stud wall, they would have to be sawn off and I can't think how to restore their load transference once they're cut. So the less destructive I can be for access purposes, the better - I reckon I'll have sufficient access with alternate boards pulled.
If the pre-drilled steel plate acts as drilling template for the ply, all holes should align fine, and the holes in the 25mm ply initially clamped in position on the joist should give good guides for drilling through the actual joist.
If the repair's insufficient it could always be replicated on the rear side of the joist using the same drillings with longer bolts but it would be nice to try for a reasonable improvement in one hit. Obviously the ideal would be to extend the entire span of the joist, or at least to the point where the advantage gained starts to fall off relative to the problem to solve, so it's a trade-off.
The only detail I can think of changing is the vertical distance apart of the two tiers of bolts. I get more mechanical advantage the further apart they are, but I ought to be maintaining a safe margin from the edge of the joist, as modern guidelines on drilling and notching imply. There again at 10mm their impact is relatively modest. I'm sure the original plumber would agree...