It appears I finally have a solution. Reaktor gets close to what I want with its sampler modules when set to "poor" interpolation, but what held me back from it for years, other than its limited save features for samples, was its upsampling limit of only four times that of the host DAW.
In the past month, Plogue gave a partial solution to the latter, and possibly the former as well! The latest few versions of their Bidule program, which also is available in plugin form, permits oversampling of VST's, meaning I can use Bidule as a wrapper to upsample even further, provided my computer is willing to be fast enough to deal with it.
Unfortunately, as just implied, the drawback is that it can easily hog a lot of CPU, even if it's just one instance. For example, I made a track for an upcoming Amnesia custom story using two instances of Reaktor oversampled by a total of 8x (4x within Reaktor, 2x within Bidule). While the high-note aliasing was almost completely gone (gone enough to not have obvious artifacts after applying filters), each instance took up an average of 5% to 10% of my CPU, which, mind you, is a late 2013 Mac Pro with 32 GB RAM and six 2.5GHz Intel processors. Needless to say, I do not recommend this approach if you make music on a laptop.
Still, the piece is available for listening on my Patreon page. You may question why I went through all the troubles with my CPU after listening to it, and the simple version of the counter-argument is, it sounds glitchy without the oversampling.
Thank you for reading, and enjoy the musical results!