I have sometimes in the past swished or gargled my "Swamp water" with Miracle-Mineral-Supplement in it, and I had 2 Amalgams at that time, so I guess it works! I never had any ill effects from doing it.
You might consider spitting out after you swish (then rinse 1 x or 2 x with water), then making another batch for swallowing ... just a thought. The stuff is certainly cheap enough that this is feasible. And this way, there should be no real concern at all about freed up mercury ions.