any attempt top capture and use the methane coming out of the dump?
That is a very good question.
Not from any greenwashed Globull warming POV, but rather a cost and efficiency one.
There are a number of places here capturing the methane and using it to power either IC or turbine engines to produce power and some co and tri gens producing heat as well.
One of these is only about 10 min away from me and produces a lot of power and was cheap to set up. They have been running it some time now and have found that even old ground nearby on the same landfill site is producing better than expected amounts of methane so there is currently a LOT of expansion under way including more community facility's that will be heated and cooled with by products of the energy generation.
I'd guess that one of these methane powered facilities would be a contender on a cost Vs return basis to solar especially the 24/7 all weather nature of gas generation as against the limited hours solar works.
In any case, I would not imagine it to be all that difficult to do both on the one site. Use the methane to fuel a generator and have the solar sitting on the top. As you would have to have the transformers/ control/ switchgear for the electrical side in place for either, making that a bit bigger and doubly feeding would lower costs and increase efficiency. You could be producing power when the sun don't shine which would be very valuable given the absence of solar at that time.
Maybe it would be possible to store the gas during the day to run the generators harder at night when there was no solar?