Version used:
Super Hang-On (W) (REV0) [!]
Before anyone asks, the in-game timer has a bug where the fractions of a second is carried over between stages. The real in-game time is determined from taking the displayed in-game time in the high score table at the end and subtracting the second fractions of each completed stage times except the last one. I will write up an explanation of the timer and how it's kind of bugged some time in the future, probably as an entire game resources page.
For reference, the RTA world record is 3:10.99 and the sum of RTA best is approximately 3:09.43.
Edit: I only found this other existing TAS of the Beginner course some time after making this run which is faster than mine in all places except stage 2. The reason I missed it was that it wasn't labelled as a TAS in the description and no comments to call out this fact. A different emulator is used but isn't really an issue since lag doesn't affect the in-game timer at all. In any case I'll probably take a closer look at this some other time to see exactly how far that time could be pushed down.
Stage times
Final stage time approximated by subtracting the sum of the other stage times from the displayed course time.
Stage 1 - 33.96 sec Stage 4 - 30.30 sec Stage 2 - 30.71 sec Stage 5 - 31.10 sec Stage 3 - 32.46 sec Stage 6 - 32.58 sec Displayed IGT - 3:11.11 Sum of second fractions of stages 1-5 - 2.53 seconds Actual IGT - 3:08.58
YouTube encode available here.