Reporting back - this is what I did:
First I clad the steel in Fireline plasterboard, screwed to noggins inserted in the web of the joists, with the underneath piece screwed up into the side pieces and Gripfilled to the steel.
I got three pieces of timber delivered from Howarth Timber, inch thick nominal (ie 21 mm). Two side pieces were 5400mm x 230mm, and an underneath piece was 5400mm x 212mm.
First I fixed one side piece. Applied lots of Gripfill, and clamped it to the plasterboard with several clamps, with short bits of floorboard used to spread the clamping force. Then I fired several 50mm pins into roughly where I thought the noggins were.
Removed the clamps after a few hours, and nothing moved. Repeated the operation with the other side piece. This one needed severe propping at each end to remove a bow. Took the clamps off the next day, and again nothing moved.
The underneath bit sat under the edges of the side bits. Applied PVA to the sides of the underneath bit, maneouvred into place with a helper, propped with some bits of wood slightly longer and went along with the nail gun, pushing firmly up and firing 50mm pins through the edges of the underneath panel up into the side panels. Once pinned it wasn't going anywhere.
I chamfered the edges the following day with a belt sander, to remove irregularities and overhangs.
One end of the steel sits on the outside corner of two internal walls, the other on an 18 inch nib of the wall that was removed. Therefore I cut the underneath panel with two 18 inch x 21mm ears on it, to go either side of the nib, so the "beam" appeared to be the same depth all the way across..
The good part (apart from everything staying up) is that the heads of the pins, being self-countersinking, do not draw attention to themselves.
What could have been better: you don't have to look very hard to see where the join is. This is partly because of knots in the timber that disappear half way across the knot, and also possibly because I ran out of 50mm pins half way through the final stage, and had to do some emergency proppoing while I found some more, so there are some minute gap lines. Having said that, the result is acceptable. The wood is a bit blond at the moment, but three years of sunlight will fix that.
Cheers Richard