I agree with both AA4PB and KA4NMA.
With regard to the GFCI breaker, it is likely that a piece of house wiring is resonant at 40 meters.
Older GFCI breakers are notoriously sensitive to RF. Newer ones less so. I had the same problem and solved it by replacing the GFCI outlet. If you go this route use a good reputable brand. Pass and Seymour seems to work.
With regard to tripping the Non-GFCI breaker, I suppose it may be possible, but I never heard of an ordinary breaker tripping out on RF.
Operating with an indoor antenna can be tricky. You are too close to the antenna and strong RF can do some strange things, particularly if you are in the same room. Assuming you can't get further away from the antenna, you will probably have to reduce power and hope for better band conditions
Hope this helps
You should do your RF Exposure calculations as well... If you have an upstairs neighbor, you are probably exceeding the FCC limits for exposure... To say nothing of yourself... See:http://hintlink.com/power_density.htm