HUD in Commander Keen is blank while recording in OBS

Game is Commander Keen 1, Invasion of the Vorticons (1.31 1/23/90)
Recording using OBS 26.0.2 (64-bit Windows), and DOSBox 0.74-2 (using output=opengl in dosbox.conf)

While recording/streaming, pressing the space bar brings up the HUD. Everything is fine in DOSBox, but HUD is empty in the OBS preview and recording output.

The strangest thing I noticed while writing this up is using ALT + TAB. Moving from DOSBox to OBS, and then from OBS back to DOSBox causes a narrow line of the HUD to render.

Moving from DOSBox to OBS, and then from OBS back to DOSBox a second time causes the entire HUD to render normally.

(Another, perhaps related rendering issue, is that during the end credits — everything looks normal in DOSBox — but when watching the recording, rendering will stop mid-word exactly 2 characters before the end of the last line, pause a solid second and a half, and suddenly snap to and complete the line. It does this for every dialogue box.)

Is there anything I can do to fix this rendering problem?