UPDATE: I've managed to get quite good FPS both in game and in the recording, with only occasional spikes, by tweaking the settings. Here's what I did that I can recall:
In game:
1. Windowed game mode
2. Borderless mode
3. 1024 x 768 game resolution
In OBS Studio:
1. Use Window Capture, not Game Capture
2. Check multi-adapter compatibility in the Source Settings window
3. In Output Settings under the Recording tab, use the H264 encoder (this is an AMD thing, not sure how this would differ for someone else, sorry) and use the Speed quality preset
4. In Video Settings, use Bilinear Downscale Filter and set to 30 FPS
Can anyone else input on this? I'm going to play around with the settings a bit more, but is there anything I've done wrong? Could I tweak this for greater performance? I'm a bit of an IT guy, but not a tech wizard, so for all I know I've hurt my performance with one or more of these settings.
Anyway, at least I've got some reasonable recording going. Yay! Looking forward to possibly putting some stuff out for the community...