Two years later, I can say I finally managed to clear the game!
EmperorIng - 13,245,480 - 2-5-1 - SAT

I have to give a little bit of props to Perikles' 2ALL video - though I have to say I am disappointed at the somewhat... inelegant solution to stage 5's final gauntlet of powerful ground enemies and their annoying bullet spreads (starting at 16:40 in the video)

. Essentially, save your bombs for that point I guess! Staying in the middle will let most of the side enemies bullets miss you - but only if you stay still. Thus the turrets in the middle try to force you into their bullets, or someone else's. In that case, bombs away!
Despite little hiccups like that, they provided a few hints to help a brother out, like a decent path through stage 6's tricky larger ship barrage, or aggressively point-blanking the final boss's shoulders - although the Saturn port's max rate of fire is much less than MAME, which made this strategy a bit more dicey and more reliant on bombs.
I was on edge during the entire final boss, because I had choked yesterday playing against it with two lives in stock. I was so mad I was ready to hurl that expensive disc across the room.

The easiest part to mess up, for me, is actually the fast, close spread it shoots when you destroy both of its arms. Despite being a simple pattern, its largeness can visually overwhelm you, and if you are too far to the side, hitbox confusion can lead to a messy death. The lack of respawn for the boss certainly doesn't help!
The second loop, surprisingly, wasn't much harder, outside of the initial shock of the first stage (and the boss's now minuscule cool-down between laser blasts!). Despite a stupid death in 2-3 (which happily lowered rank), the game proceeded normally, until I stupidly ran into one of the bullets from the octopus ship at the beginning of stage 5. Had I survived that I think I could have pushed through respectably, at least until the end of the stage.
One thing I have to call the game out on, which I found bad even years ago: the octopus boss of stage 3. Few shootemups that are this long can afford to have a boss so soul-crushingly
boring as this one, especially with an HP pool that must be more than the game's other 5 lesser bosses combined. I have found no way of making this fight go any faster, as the tentacles easily absorb the brunt of your offense. So what are you left with? Boss shoots, tap left; boss shoots, tap right; boss shoots, tap left; boss shoots, tap right. I will kid you not when I say that I have dozed off to this boss on runs, and sometimes
it didn't matter because my muscle memory kept me alive while my eyes drooped shut. What a terribly dull misfire in a game that is otherwise filled with interesting and unique enemies (the highlight boss being the "boxing ship" that attempts to punch you out of the sky).
All in all Shienryu is a great shooter. It feels like a better extension of older Toaplan games than some of Toaplan's own later games (e.g. Twin Cobra II or Tatsujin Ou).
EDIT:
Interest glitch in Saturn port of Shienryu:
During my failed practice run, I soft-reset the game during the credits sequence (ABC+Start). When I started immediately afterward, the Stage 1 BGM was replaced by the credits! I thought it was kinda neat rolling through stage 1 with the moody synth-sax midi playing in the background. However, no other tracks would play, forcing me to fight the boss in eerie silence. I could only get the music back by turning off the system and restarting. Must be a weird glitch of how the Saturn streams the music data off the disc (instead of playing redbook tracks).