I don't have quite as large a difference as you (265 70 16) but my experience might shed a little light. A few weeks ago I had a flat out on the I-10 freeway in Az near the New Mexico border, more than 100 miles from home. I tried driving home with the spare, but any time I got to 35mph or so the TOD started going nuts and locking. I finally pulled into a Big-0, and two hours after closing a Big-O salesperson was willing to come down and sell me a full-sized tire/spare.
Driving with the stock spare was aweful!
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