Will excess oil damage a Briggs & Stratton 375 quickly?

I find the dipstick on a Biggs & Stratton Sprint 375 very difficult to read. Yesterday I topped up the oil (30grade), started the mower, it ran well 15 min, then smoked a bit & snuffed. Spark plug has about 3 hours on it since new, heavy carbon, oiled. Cleaned it -wire brush, kerosene rinse then auto. brake cleaner rinse. Put in back in dry. Drained the oil by sucking out with plastic bottle and tube, (was dirty anyway) refilled with new correct 30 grade oil. did not tip the mower at any point. Started, ran fine 10 minutes, snuffed but without smoke this time. Spark plug oiled. Cleaned plug again, started, ran fine 5 minutes and I shut it down myself.

Motor is about 8 years old and has not done a lot of work since we have had near permanent drought and sprinkler restrictions since 2001 and there is little growth here (Canberra, Australia) May-September in any case.

I'm presuming the initial oil top-up was slightly, not grossly above the correct level. Will this damage the motor severely or permanently?