I got it! Thanks to several of your suggestions and a bit of luck.
When someone in the "Light or heavy fighters" thread suggested Ripper mines, the latest Starflier save that I had that could go get them was at Kyushu, meaning I had to do the Tekagi's Transport mission again. Having to kill those Weapons Platforms again (remember that's the one ya gotta do fast or you fail) made me realize again that the fastest way to deliver damage is keep your guns trained on the target and shooting; don't muck around with strafe passes or mines when you don't have to. But when the powerplant and shields run down, get away with a thruster engine kill and let them recharge.
I also had to re-do the freelancing period at Kyoto. Flying random missions, I happened to get both wings shot off. Thanks to your suggestion I left them unrepaired, and it did make a noticeable amount of damage I took in dogfights, especially the Tekagi patrol before the arch.
I won the Arch mission on my third try this time.
Someone else in the other thread mentioned to pay attention to the Kusari battleship - an excellent point. As soon as possible, I flew right up to each of the two generators on the opposite side from it, parked (using reverse and thrusters to move around slightly), and unloaded the Scorpions and Drillers into them, and they went down easily.
The two generators nearer the battleship were harder - and by then most of the Dragon ships were down and the entire enemy fleet was shooting me and Ozu. I couldn't sit still now; had to keep flying gun runs punctuated by a couple Driller mines as I passed the generator, then engine kill, turn, and repeat. The most important of your suggestions here was to use missile countermeasures liberally and often. I banged on the C key two or three times whenever the incoming-missile sound came, or if I was drifting backwards at the time, shot down the missile. Only got hit by about 5 missiles during that sequence, and most of them hit a just-restored shield, taking it out again but because they hit the last bit of my shield delivering much less than advertised damage.
Made it into the arch with 5 nanobots to spare.
Then in mission 10, thanks to the Driller mines, I scored a battleship kill in the Sigma-13 fleet battle. In the battle outside Bruchsal, I actually died once due to carelessness (one enemy ship left and I whacked myself with my own mine.)
The experimental battleship was much easier than I expected. Just kept flying back and forth along the length of the target, shooting it on the way in until the powerplant ran down, then dropping 4-5 Drillers along the length of the battleship. The minefield on the way out had me much more nervous than the earlier part, with finger poised over the shield battery button the whole time.
I'll try Mission 11 tomorrow; this one will be a doozy too, although during most of the fights you can pretty much circle around and let your allies take out the targets.