Full run through 2 loops of R-Type III (Normal & Advanced/Hard Mission), my final score was 1,379,580. This was captured off a real SNES console, no emulation or cheats were used.

Loop 1 (Normal)
00:00 - Start
00:41 - Stage 1 - Catapult Dimension
06:47 - Stage 2 - Acid Creatures
10:41 - Stage 3 - Heavy Metal Corridor
15:09 - Stage 4 - Fire Cask Factory
20:33 - Stage 5 - Bionics Laboratory
25:44 - Stage 6 - Galaxy of Abyss
33:16 - Final Boss

Loop 2 (Advanced Mission)
0:35:58 - Stage 1
0:43:34 - Stage 2
0:48:40 - Stage 3
0:54:00 - Stage 4
1:01:41 - Stage 5
1:11:03 - Stage 6
1:18:33 - Final Boss

I had some very, very stupid deaths in this run, but did manage to pull it together near the end (including recovering from the boss rush with an underpowerd ship).

This is a pretty cool game, there are some slow spots in the first half but the action picks up considerably near the end. Although I wouldn't rank it as hard as Super R-Type, it's definitely the better and more enjoyable game of the two.