There are a lot of things that are possible, but they come at the cost of a substantial increase in the time to run the script. That may not matter if you're only running it on a couple of games, but if you have 3500 files to run through (roughly the daily Goko archive at this point) and you add a second to each run, you've added an hour of processing time.
Moving the game summary info is a reasonably resource-intensive process, surprisingly. You need to grab the game summary section and move it to the top. But, since it's multiple lines, you can't just do it with a stream editor unless you use some black magic like removing linebreaks from that section or adding tags to each line in that section. There's probably a couple of writes of temporary files to the disk in order to make that happen. Then you splice the new header into the old file, requiring another write or two. You may then need to undo your black magic edits.
(Also, I've heard mixed opinions on listing the game summary at the top. Some people like the surprise of finding out who won at the end. I'm not in that camp, but since it's an opinion and changing the parser to move the game summary is hard, I'm defaulting to what will let me be lazy.)
The long term solution is for Goko to change the log file. Whether they go all the way to coloring the logs or not, fixing things like listing the opening cards, the trash contents, and the value of alt-VP sources are ridiculously easier if they're done in the original.