Well all MPC's are digital samplers so they will sound digital as well. The 2000xl is actually VERY clean, the MPC's with the lofi sound you are looking for would be the MPC60 or the MPC3000 but those work even slower. What you can do in Maschine in 30 seconds will take 30 minutes+ on those old MPC's. Maschine does have an MPC60 mode that helps. Have you tried a virtual tape machine plugin like Slate virtual tapes
http://www.slatedigital.com/products/virtual-tape-machines/ or Uhe's Satin
https://www.u-he.com/cms/satin both would help. Seriously I have owned many MPC2KXL's over the years, and while the pads are great, and its nice to have. I can not imagine using one again.
Also I found this article very helpful in understanding the MPC "sound"
http://www.attackmagazine.com/features/interview/roger-linn-swing-groove-magic-mpc-timing/ I can even get it out of just Reason these days. In fact this song
that I made years ago was me pushing Reason to try and get the MPC sound. I think that song is all Reason 4, but listen to the drums, they sure sound like they could have come out of an MPC.