Whatever you decide to go with, make sure it meets minimum code, just much safer and no liabilities.
The 2x3 ripped and routered corners does make a nice handrail. Make sure it is 1-1/2" x 1-7/8" when done to meet the max. perimeter size per Code. 2-1/4" = 6-7/8" 2' = 6-3/8" still larger than max. of 6-1/4". http://www.arcways.com/pdfs/IRC2006.pdf
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17,000 dryer fires a year, when did you last clean the inside of the dryer near motor or the exhaust ducting?