We don't have much control over how fast Adobe's software produces a DNG for Photo Mechanic to use the preview from, we simply call their application and wait for it to provide a file. If it is unusably slow, I would recommend converting the images through Adobe DNG converter first and then using the files that it produces. Though it may take some time, it would mean that there is always a full-sized preview in the new files, so if you view them in the future in Photo Mechanic they would not need to be re-rendered if they had been flushed from the Render Cache.
I'd also recommend giving feedback to the manufacturer of the camera. If they embed a full-sized preview in their DNG files, no extra step or converter would be necessary.
