I can sympathize with the housing issue. My gf and I are looking for a rental in the Eldorado school district (my son's a very active student there and it would kill him if we moved out of district and were denied a transfer).
We've found a few lovely homes for rent, but unless you apply for them within hours of posting, they are gone. I can't speak directly to your question about Jackson M.S., but we have had very good experiences at Eldorado High. I know that a little bit of the Jackson district feeds into Eldorado. The rest feeds into Manzano.
My youngest attends Cleveland Middle School (which feeds into Sandia and Del Norte), and we've had pretty good experiences there. I am convinced, though, that with APS you get out what you put in to your kiddo's education. Demand that they get involved in something, anything at the school. For my sons, it has been band and NM MESA.
Good luck with your search!