Man, I know by the 90's MPCs were getting mad popular, but the legendary sampler the SP-1200 was used for tons of 90's New York sh*t.
I heard DJ Quick say he used it for his 1st 2 albums.
I guess some west coast artists were doing it as well.
It samples at a max rate of 22k.
Now your MPC1K samples at 44.1k.
I can't remeber if or how the MPC1K reduces the sample rate.
I KNOW that if you get or have the JJOS2 for it than it adds this option, because I had it & used it allot.

I heard some producers say the SP12 colored the main sample in a way that made it sound like magic in the mix.
I hear more often producers say it gave the drums that grimey lo-fi sound & that it is why it is in the sampler hall of fame.

I think 'deRaNged 4 Phuk'dup' posted something worth reading as well.
A sample w/ boom bap drums comes fairly easy for me, but a composed synth beat is near impossible for me to do.
I can't play strings or chords to save my life, but I feel like I hammer out drum patterns w/ the best of them.

I got an sp-1200 vst plug-in that 'supposedly' colors your sound like that sampler.
I use to run my audio through it before it hit my sampler.
That won't help much if your coming off a record though.
If you want I can try & dig it up for ya. pm me.
If you don't have JJOS on your MPC you should it is worth every penny!

Thats all I got, but good luck finding the sound you want.