This took 460 GPU-hours (so about ten days on two GPUs).
First I ran a calibration job to see what stage_1 value was required to get about 20 stage-1 hits per second; the answer turns out to be about 1e27. Then I ran some short ranges (1-2M and 2M-3M), took a 1% sample of the stage-1 hits and ran -nps with a high stage2_norm, sorted by output score and reran on the whole set of stage-1 hits with the threshold equal to the tenth-best output score in the sample - that is, I was aiming for about a thousand stage-2 hits. Once I knew how long the short ranges had taken to run, I ran some longer ranges (3M-17M on one GPU, 17M-30M on the other) and repeated the process.
After running -npr on the thousand-or-so stage-2 hits, I sort by E-value and note the hundredth-best as a plausible threshold for the next job.
So for 114!+1, difficulty 186.4, the stage-2 threshold I found good for the long ranges is 1.2e+25 (this actually got about 2000 hits), and the hundredth-best-E-value on both ranges was about 2.6e-14.