Did you try testing the coils with a multi meter? I think the resistance thru the primary windings should be ~.5-2.5ohms and the secondary ~2500-5000ohms.
That Turf-Guard 10W30 isn't exactly made from unicorn sweat. I've been running a group IV (PAO-based) synthetic in various small engines for decades. Synthetic vs dino or any blend of the two will not kill these engines. I don't like modern automotive oils in small engines (with all the sliding contact and the reduction of anti-wear additives like ZDDP) for longevity but immediate harm is certainly not a thing.
I don't like using resistance to test coils...VERY unreliable, doubly so on an intermittent problem like this. You can do the test, might get lucky and get a difinitive reading like open, or continuity to ground, but usually what happens you get a reading that is just outside of their specs, and a new one doesn't fix it...that crap doesn't fly at a dealership (at least an honest one) so coils (of any kind, not just ignition coils) get condemned on voltage test instead...but sometimes those numbers can be hard to come by, Honda was tight lipped about voltages back in the day, heck the only way I found out that they actually had voltage specs was by going to their tech training, the American Honda guys shared the numbers with us that Honda Japan kept secret (and they wrote the manuals then) I think that info is much more available since then (I dunno, been away from it for over 18 years now)
Thought about it, but there are big warnings all over service manual stating "DO NOT TEST THESE COILS WITH MULTIMETER OR STANDARD OHMMETER. TESTING THESE COILS WITH ANY METER OTHER THAN JOHN DEERE XXXXX WILL CAUSE SEVERE DAMAGE."
Yep. Sorry, I should have been more clear. I have no problem using dino or full synthetic, although I usually stick to Deere OEM fluids for Deere machines, since they run some pretty tight specs. My mention of it was not because I loaded full-synthetic, but because I had mixed the two, probably approaching 50/50, given how bad the machine was leaking dino thru front main seal, and how much it took to come up flush again. I've been told before to use one or the other, but never mix them. Not sure if there's any real merit to that thinking, but figured I'd mention it, in the spirit of full-disclosure.