I ended up accidentally taking off the top of one of my flashers while trying to pull it out. Oops. But that ended up being a lucky result because I was able to see how they oriented the resistors - they were wired right to the base with the leads of the resistor being the wires used to make contact with the socket.
As a result, it was a pretty easy swap. The originals were like 20 Ohm or something surprisingly small. All I had on hand in the small footprint and range were 220 Ohm. Gave those a shot and it's MUCH better. Almost perfect, in fact. I think the shield flashers might be a tad low but I just wanted a subtle effect there anyway.
These were using the NiftyLED 906 flashers. I suspect other flashers are different.
At this point I think the remaining flashers are in the Borg ship and around the playfield but I rather like OLDPINGUY's option since it looks flat. I bet that would go really well under the Return To Duty. So I'm pondering that.
For now, though, all is good!