The strip method should not need any trimming.
For 2 ½" HSTs you won't need the strips to be 2 ½", I think 2 ¼" is wide enough.
Try a test piece (this is what I'll be doing later - testing widths I mean).
Just join two fabrics along both sides, place a normal square ruler so the 2 ½" marks are lined up on the seam line and cut on the blue lines marked. Turn ruler around and cut from the other side.
If you begin with a suitable width you can even cut off the dog ears as you go & no waste.
The edges will be on the bias, but try starching first to keep them firm.
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The strips could be cut at a 45 degree angle and then sewn together.