We have seen several reports, from various cities, for locations that are very close to extremely strong signal sources as shown in your reception prediction.
The levels shown in this case call for 20 to 40 dB of attenuation between the antenna and tuners input. I've had experience with locations such as transmitter sites, where RF tight enclosures were required to house and shield electronic equipment from the RF coming off the transmitting antenna. I've got several HDHR tuners, but have never faced intense RF levels that caused interference due to direct penetration from the air into the tuner.
What happens when you disconnect the coax from the tuner input? If you still see very high signal strength indicated by the HDHR utility then you may need to look into RF shielding for the tuners, over and above the attenuation of the signal from the antenna(s).
http://forum.tvfool.com/showthread.php?t=820
I would expect best results will occur when the antenna(s) are aimed at the source (the TV transmitter antenna) to receive the highest quality signal possible and then attenuated to a level that does not overpower the tuner(s). The idea is that if you aim off to the side, you're are going to receive more multipath interference which lowers the quality of the signal. A high powered low quality signal is no better than a low powered low quality signal as far a the tuner is concerned.
For others reading this thread, this is an illustration that 'high signal strength' is not synonymous with 'high signal quality'. Poor reception can be the result of too little signal, but excessive signals levels can also result in poor reception due to overloading the tuner. A common, but often erroneous, assumption is that if a signal is 'weak', amplification will cure the problem. Only if the 'weak' signal is of adequate quality could you expect amplification to help, and then, only if there is substantial loss in cable and splitting between the antenna and tuner, or possibly a poor quality tuner.