1,275 (1,251) Stedman Caters

Donald F Morrison (no. 2337)
231456789  1  6  8  15  16
214365789         (a)     
123465        s  s   -     |
125364           s   -   s | A
124365                   s |
214365978  -  s
124365             A
124365879         (b)
214365             A      
round next handstroke
(a) = 1.4.s9.10.11.13.14 (14 sixes)
(b) = 1.s7.18

Reduce to 1,251 by calling (b) = 1.s3.4.5.6.8.9.11.12.13.14 (14 sixes).
Either length contains all eight near misses.