We already know that small networks beat bigger networks in fast games, but we might expect the bigger networks to catch up in slower games. Let's pretend that each engine/network combination has an "baseline" strength (how well it can play on minimal thinking time) plus an ability to get stronger with more time. There will be diminishing returns: you'd expect a big difference between 1 minute and 10 minutes, but not much difference between 60 minutes and 69 minutes. But the strength is theoretically unbounded (Monte Carlo search converges to the best move given unlimited time and unlimited memory).
So a half way reasonable model might be:
where b is the baseline strength, t is the thinking time in minutes per player per game (absolute time, because I don't want to get into complications around byo-yomi), and alpha represents how well the engine/network can make use of extra thinking time.
At 1 minute time limits, t=1, log(t)=0, so b is the just the 1-minute Elo rating. Then we can calculate alpha as (5-minute Elo minus 1-minute Elo)/log(4). (For me, log means natural log, because I did too much calculus as a teenager, so log(4) is about 1.386.) And then the expected 20-minute rating from this model would be b + alpha times log(19), or b+2.944 alpha.
If we have gnugo at 1500 on both rating scales, then it gets alpha=0, meaning that gnugo gets no stronger when it thinks for a long time. Worse, a few of the weaker engines get negative numbers for alpha. I don't believe that, so I'm going to subtract 200 from all the 1-minute ratings, just to get some more reasonable alpha values.
Finally, this projects pachi_nn to be about 3300 in 20 minute games, which isn't realistic (it's nowhere near pro strength), so I'm going to subtract a few rating points from the results to put pachi_nn at 2400.
Then a few lines of R programming gives these results:
So we can see for example that LZ_phoenix comes 17th in 1-minute games, but 9th in 5-minute games, giving it a big alpha value (it's making great use of the extra thinking time), and we'd expect it to shoot up to 4th place in 20-minute games. On the other hand, LM_E8 (with a 128x10 network) did better at 1 minute than at 5 minutes, so its alpha is lower, and we'd expect it to rank even lower at 20 minutes. Then again, the alpha values for LZ 141 and 174 don't look quite right.
This is a pretty simplistic model, so I don't expect the results to be at all accurate (we can tell it's not right by the way gnugo has dropped 500 points in the output), but it's interesting food for thought.