Ken, just a collection of thoughts; might not help much.
1. 15min contact time is for viruses and bacteria, if i'm not mistaken. 30min giardia and maybe longer for crypto (up to 4hrs for some chemical disinfectants - don't know about AqM). Couldn't remember or find and real numbers for AqM, but somewhat similar Cl-O2 products have times similar to those i mentioned. You may want to wait longer before ingesting.
2. the MSR "thingy" you mentioned is called MIOX. It too is a chemical disinfectant like AqM. It may not work any better for you than AqM.
3. Did you mean Micro droppers or Mini droppers? The Mini is 11drops per liter. Is Micro the same or is drop size smaller??? Don't know. Of course if one halves the dose, the contact time is doubled, so keep that in mind - you said that you were using 10drops, so a tad longer contact time is in order.
4. Not sure of all the chemistry involved, so the following could be totally off-the-wall. I don't know the half-life of the chems in AqM, nor if they make it through the stomach, and upper intestines intact with reacting with various digestive enzymes. If the chems are still active when hit your intestines, they can kill off normal intestinal flora, which account for ~20% of the volume of stools, IIRC. This is why "broad-spectrum" antibiotics can give a person the runs. Basically, IF this is happening, you are disinfecting your intestines. This will cause the runs. Maybe you are sensitive to this chemical. I can do the same thing to myself with too much wasabi, hot chinese mustard, or jalapenos. Yogurt with active cultures often works well to resolve this issue. You may want to wait longer before ingesting the water to give more time for the chemicals to break-down (again, i don't know the half-life so i can't say how long, or if the wait would be prohibitively long).
5. The 24hr onset of your runs may lend credence to #4 above. Crypto onset after ingestion is 2+ days (sometimes a week). Giardia is 1-2weeks onset after ingestion. Therefore, if you are being precise about the "next day" onset, neither is the most likely candidate - unless you contracted them before you began your hike, or encounter a more rapid onset strain of Crypto. Crypto can be relatively benign and in some areas up to 85% of the population has been exposed to Crypto - most with no ill effects. If your water at home comes from a well, you might want that water tested, and/or install a water purification device on your home potable water system. Do other family members, if any, have any similar issues? Visitors to your home? Just trying to determine if symptoms are related solely to you and only when your in the field.
6. Can there be chemical pollutants in the water (before you add AqM)? More likely, perhaps, in some places out my way, perhaps less likely where you live an hike.
7. I've used UV-C purification. Keep in mind, that just like chems, UV-C, at the dosing levels produced by SteriPen and AquaStar units, won't kill larger parasites (flukes and tapes). Approx. 28x higher dosing is required for 98% inactivation - not a very high pct. actually - i like 6 9's, or one in a million (99.9999%) inactivation. As little as 1 Crypto cyst ingested in volunteer human testing has produced symptoms - larger parasitic organisms probably also require a similarly small load to produce infection. UV-C, however, it will inactivate viruses which a simple mechanical barrier filter won't eliminate. The coffee pre-filter Douglas mentioned is a very good idea. However, i'm not sure the "pore size" of the metal ones is small enough. 25micron pore size is the absolute max and is right on the edge for hydatid tapes. A paper coffee filter is uncontrolled so pore sizes vary with 5-15microns being typical, so this would work, but is not very robust and slow to gravity filter.
Sorry i can't be more help.