eliminator I would say definately you cannot use a sat inline amp, pretty sure it has a high noise rating.
Normally RG6 cable has better shield and lower loss, but like I said with your short cable run I dont think you have any significant signal lose.
Rg59 only loses about .75-1.5db from 75'+ compared to RG6 and a little more over longer distance.
Its hard to suggest how to improve your reception without seeing how and where your antenna is mounted and how much of those trees blocking your signal.
Did you make up your own cable and put on the ends yourself ?
A important tip for readers here who are not experienced, make sure that you did not strip away the braided ground wires.
I pulled back the braided shield so you can see better.
Was the white center part(dielectric) of the cable butt right up against the inside of the cable connector and then you have atleast 1/4" of of the center copper conductor sticking out.
I have seen many installs that the person does not know how to strip a cable properly and stripped away all the braided wire and then the white dielectric was not butt flush with the inside of the connector.
This resulting is weak signal from the Buffalo stations and also weaker local 8bars on a Samsung 451 instead of 10 bars.