The heater core is not complicated. It's either flowing or it's not. did someone else flush the core, or did you do it? Do you know if they (or you) removed the hoses and flushed the core independently? Back and forth?
If there is a bunch of gunk in the whole system, the heater core may be where it's all ending up when the coolant is circulating. If you have rusty gunk circulating around your cooling system you'd need to find the SOURCE of the crap. So, cleaning out the block is not a bad idea, at least you can eliminate that as a source of crap.
Unless the core is leaking, I would not bypass it. Has anyone put any stop leak stuff in there that you know of?