PCR a plasmid with self-complimentary regions?
From experience, your present problem will not completely go away no matter what you do.  The idea for asymmetric PCR is not a bad idea. However, you will only get linear amplification of the desired product from the initial single primer, so you will not "see" any product even after 30-40 cycles.  This first single primer PCR might also cause downstream problems with amplification of undesired products made during the second PCR (junk products).

I agree with comment #1, but then neatly cut the "visible" "good" band out of the gel.  Suspend (crush) the agarose band in sterile TE buffer, and then use an aliquot of that as template for a secondary PCR (use equal primers - maybe 30 cycles).  This should provide more than enough "good" starting template.

Alternately, you could design a new forward primer that does not have a bad secondary location on your plasmid.