I use I-joists from the lumberyard. Relatively cheap, lightweight, flat, and you can get them as long as you want. You don't need a super deep one since it will be supporting little weight in comparison to its intended purpose (floor joist). Screw on some legs, bracing and a top, and you're ready to go. On something that long I'd recommend at extra set of legs in the middle not so much for vertical support but rather to keep it from moving/flexing horizontally (bowing). Screw the feet to the floor.
As for extending your current strongback I can't see the pictures you posted so unsure of the construction. I think it would certainly be doable, especially if you added an extra set of legs for support under the splice.
For setting up forms I prefer a method that doesn't rely on the strongback for vertical alignment. I use a laser level so it doesn't matter if the strongback has has some high or low spots. A similar method would make your strongback extension much simpler since it wouldn't have to be a perfect transition, it only needs to not move during construction.
Alan