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Yeah, back to back but validated as two separate rides.
Eg - start Meridian Hills at 0700 from Greent St Green, finish at 1900. Get second receipt from same place then ride Down to Downs.
I can't think of 300 I can pull off in a day that attracts AAA and be able to get home and sleep enough for work the next day, and I can't DIY a 300 and claim AAA without a GPS.
This fiendishly simple plan allows train home from finish if necessary too.
If you rode them back to back?