Tuner sensitivity on the microHD is the best of any consumer receiver I have personally tested.
The problem with using a 6 foot dish (I am guessing you are suggesting on C-band) has very little to do with tuner sensitivity. The beam pattern of an undersized dish that is not 2 degree compliant is not narrow enough to produce a ratio of good and desirable channel signal verses the surrounding noise.
Garbage in .... Garbage out.
These feeds are typically calculated for a link budget using a minimum 7 meter downlink. I am surprised when reported 16 and 32APSK feeds are received on anything smaller than a 3-4 meter (10 foot) dish. If you don't have an adequate dish size for the link budget, there really is no work around...