Sharp corners create potential for cracks, or so I've been told. If you kept the patch piece a rectangle and just rounded the corners, you should be okay. Drill holes where the corners would be at the spot you're cutting out to, again, avoid sharp corners. Then cut between the holes. Bevel the edges, like you said, for the best penetration.
Although, it's hard to tell from the picture, the spot in question doesn't look all that bad IMO. You'll have an engine crossmember in there which will add way more strength than a patch piece.
And, a $10 patch piece doesn't sound that cheap to me. I can get a ten foot piece of 3"x 1/4" strap for $18 or so.