Wall plastering in Taiwan: Plaster sets VERY fast (10-15min). What can I do?
The working time of setting-type plaster is a consequence of that plaster's ingredients. In the US, setting-type drywall compound (e.g. Sheetrock Easy Sand) can be had in a wide range of drying times from 5 to 210 minutes. If your mix is getting crumbly after 15 minutes, you might just have the wrong product.

Combining setting and pre-mixed compound is not something I've seen recommended. Final dry time, strength, shrinkage, etc. will be hard to predict. Perhaps you can work out something that does what you need this way, but I think you'd be better off finding a compound that gives you adequate working time when following manufacturer instructions. You can also find plaster retarder and accelerator that should let you adjust the setting time.

Alternatively, you can try to make do with what you've got by mixing setting-type compound and quickly filling the big cracks, and then top-coat with the pre-mixed or drying-type stuff. That will let you cut out a bunch of the waiting, but then fine-tune with a slower-drying plaster.