Wanderer - Here are some things to try:
1) Get a STIFF plastic brush, or even better, a brass bristle brush. You want a brush that has bristles about 1 inch long. You can find both at hardware or big box stores. They cost less than $2. Below is a link for one. These brushes can get into wood pore and clean out ols paint. Steel wool doesn't work so well, as you've found out. https://www.all-spec.com/UserFiles/Imag ... _WebXL.jpg
2) At a hardware or paint store buy a cheap plastic drop cloth - cheapest they have. Apply some stripper to areas with "stubborn little bits", and then wrap the entire drop cloth, or pieces of the drop cloth cut to size, over these areas. Let it sit for 3 - 4 hours. The plastic prevents the stripper from evaporating quickly, and helps it remove more of the old paint. Remove and discard the drop cloth (set it outdoors overnight to prevent any spontaneous combustion before discarding), then use your bristled brush to get rid on the stubborn bits of paint.
Hope this helps