I ran a bunch of trials between your last two changes. I haven't analyzed the results, but it seems the "FastSolving" profile is nearly optimum for both the internal sexysolver and astrometry.net.
I didn't run ASTAP solutions because an early run on blind solves (with jpegs) ASTAP failed. There was a message about atk-bridge missing; however, it was installed and I got the same message after installing the -dev package. A "locate atk-bridge" gives the following: