How to support the subfloor around a toilet between I joists
For Future Viewers:

Right idea, but WAY too complicated for minimal support &amp; no screwing for the flange. With NO FLANGE in place, build a frame first, not piece by piece in the floor. With a Flange in place you'd build it without the right side's {bottom} joist attachment so you can dry-fit everything &amp; finish inner attachments to then LASTLY screw to the joists.

Stand up 2x4's to be attached to joists LAST. Then, bridge the Stand-Ups with 2x4's On-Flat. You screw through the Stand-Ups &amp; into the ends of the On-Flats (do just the left Stand-Up {top} configuration if a Flange is in place).

Then, you bridge the On-Flats with a shorter On-Flat. First, screw that in from the left Stand-Up to hold it in place &amp; toe-nail screws on either end at the Flange side. Also, toe nail what can fit On-Flat on the right side {bottom} of the Flange Finish by just screwing outward (&amp; angled upward for this Askers I-beam pictures) through the Stand-Ups &amp; into the joists.

This should be snug to the Flange's underside collar or the drain pipe, depending on your subfloor elevation. The On-Flats even allow you to cut or drill the platform frame for an actual tight fit complete circle. Of course, adjust this proven design to your actual application.