Burnishing is my preferred method for finishing. As you have already found, there are a number of tools that can be employed for the process. Agate and steel burnishers are great- especially for edge and spot burnishing, and for scratch repair. Having a number of hand burnishers with various shaped edges and contours is very useful. I found some really nice burnishers in Japan, that are almost like fat needles, and come in a few sizes. If I can find out what to call them, I’ll send the info your way.
The biggest issue you will find is that burnishing for extended periods of time is very hard on your hands. The older you get, the more you will notice…
However, your question of un-reached areas is one that needs resolution. For an all-over burnish, that will knock your socks off, this is my method:
Fine sand with sanding cloth or foam (I use 3M paint polishing sponges in Ultra fine and microfine). Use the highest grits you can locate. Typically 800-1000 is good. Finer grit is better if you can locate it.
Once I have inspected my piece and determined that the surface is just as I desire, I place my piece in a vibratory tumbler loaded with stainless steel polishing media. I use a mix of balls, saucers and pins. 5 pounds of media is adequate for most pieces.
My tumbler is a Raytech TV-5. I place the media into the TV-5 with a small amount of water and a low-suds detergent, or a few drops of blue soap (50/50 laundry detergent & household ammonia.) The soapy water acts as a lubricant. Rio sells some specialty solutions for vibratory tumbling, but I’ve never found them worth the money- YMMV.
Tumble your piece(s) from 15 minutes to an hour, depending on the size and complexity of the surface. You cannot believe how amazingly bright and gleaming the metal will be when it is finished this way. And the best part is that it is incredibly gentle and will not thin your metal.