Minimizing subfloor opening for stairs

Hello,
I'm adding a staircase to a wood frame house, and since space is tight, I'd like to minimize the size of the required opening in the subfloor. I've determined where the staircase headroom will start to intersect the 2x10 floor joists and framed an opening. However, the opening in the subfloor could be smaller than this opening in the joists, because of the height of the joists.
Now the typical subfloor won't span the 3' wide opening required for the stairs. So what is the best way to support this subfloor extension? I have a few ideas below, and I'm looking for guidance as to which one(s) would be practical and strong enough.
Thanks, Wayne
(1) Add one or more 2x6, 2x4, or 2x3 headers across the opening, just above the required headroom. The 2x6 or 2x4 could be attached with joist hangers; not sure how to attach the 2x3.
(2) Cut a bevel on the edge of a 2x10 or 2x12 and install it as a tilted header across the opening, following the angle of the required headroom. The bevel would allow the subfloor to sit flat on the top of this tilted header. For extra support, perhaps install mitered blocking between this tilted header and the orthogonal header.
(3) Add a subfloor material that can span 3' (such as 1 1/8" plywood or a 2x) between the joists up against the existing subfloor. This could be supported by stair angles such as Simpson TA.
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What ever one does, code requires 80" clearance above the plane determined by the nosing on the stair. The use of the area above the stair plays a big part in how you maintain the 80". I've seen closets with the floor raised above stairs; walls with the bottom plate 'echoed' below the sub floor and fastened to support the sub floor. T
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