How to wash amaranth before cooking>
It sounds like the only problem is the amaranth grains are too small, nothing else?  

You might use a cloth instead of (or as well as) a colander or strainer.  Cheesecloth might do, especially in layers, but even a fine woven cotton or linen cloth will be just fine, as long as it's clean.  You can line your colander or sieve with the cloth, wash the gains as you need, and let the water drip out, or wring it out, as much as you need, and then proceed to cook. The cloth can be simply upended over your cooking pot, and any remainder brushed out while still wet, or it can be allowed to drip dry until it comes cleanly off the towel.

Alternatively, if the seeds sink rather than float - you can wash them in a bowl of water, rub them around, and wait for the grains to settle in the water, and then decant the extra water from the top of the bowl.  You might take two or three changes of water to be sure the grains are clean, between the need to rinse and the difficulty draining all of the water out when you drain it - but again, you can scrape into a bowl while drained and wet, or pour into a bowl (with whatever water or liquid the recipe calls for).  You might even use this step to pre-soak your grains a bit, that might even help with the extra time cooking you mention.