Please note that this does not make samples sound like an Amiga ie it’s characteristic crunch and depth,it’s just lowering sample rates and cutting off top end and turning off interpolation .Believe me when I say the Amiga itself has a very specific type of sound, full of artefacts and noise floor and all sorts of lovely stuff goin on.While this is a great technique or sample processing(one which I use a lot) It doesn’t sound like an Amiga which is why people like me hunt them and buy them.However if you just want something close, any old smelly bit crusher will do.
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I respectfully disagree with your view. Renoise can do exactly what OP is after.
Here’s a boring demo I made, two breaks and a synth played by both an Amiga and Renoise. Amiga recorded straight into an interface, Renoise rendered at 88.2kHz and the two stitched together in Audition and resampled to 44.1kHz for upload.
It demonstrates how similar they can be made to sound, and also what OP meant by “the way that playing the sample at diff pitches affects the sound. This pitching sound was always such a big factor of what made the Amiga sound so rugged” Post info | SndUp (This hosting service is quite new and doesn’t look polished but it has potential.)
Amigas definitely have a sound - but it’s a sound that can be mimicked very closely.
My A600’s crunchy synth tones played back at C1 are perceptually indistinguishable from the same source samples being played by Renoise with the suggested instrument settings. If it wasn’t for the Amiga’s clicks at the start of playback and some 50Hz hum I wouldn’t be able to tell them apart.
There are slight tonal differences. Overall Renoise has slightly more upper HF shine. But the difference is small, and everything that makes the Amiga sound special is there.
Other considerations such as the noise floor and distortion only have a minor effect and contribute little to the overall sound.
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I agree with most of what you say,but I just don’t agree with the statement above.I don’t know if you have a variable sampler for Amiga?The noise floor and distortion for me are the biggest factors in the sound along with aliasing and all that other stuff.The noise floor I inflate with limiters,it makes the sounds fat and super dense along with compression.Also distortion incurred by signalling hot radically changes the sound, not only this but it behaves differently at different sample rates giving different tones and what not.The other thing the Amiga seems to do really really well is adding texture and depth.It turns a flat sound multi dimensional as soon as it’s sampled.Other samplers do this too but I find the Amiga very special.Accounting for the changes in sound at different sampling rates would just be so difficult and time consuming.My thoughts are summed up like this.You can sound close to an Amiga with just a plain bit crusher.My suggestion would be to look out for an a1200 with some kind of sampler.I doubt anyone looking for this type of sound would regret it.Seriously it’s like a magic box 
i know its not technically accurate but Tal-DAC vst gets you into that lo fi artefacty convertor territory you might have some luck there