The single speed again

I keep changing the rear change-ring on my single speed bike to gear the thing higher. My rate limiting hill is Lilyfield hill, which is a real heart starter in the mornings. My journey to the current high ‘gearing’ has been in a few increments, each new chain-ring being adopted only when my legs adapt to the stress. They, the legs, are getting pretty strong. The issue is, that after a few durries and schooners, the plan all goes to pot; I can’t get the bike over a speed-hump.