How do I match the audio and video streams in my video file with the audio I recorded separately? I record audio separately using an audio recorder and video separately and they usually sync up later in the NLE painlessly.

But there's one particular old digital camera I have that always seems to play back (both its audio and video) a bit slower than the audio I record with my audio recorder.

I must underline the fact that the audio and video streams of the digital camera themselves are always in sync. It's just that the audio (and video which is in sync with the camera's video) from the digital camera is never in sync with the audio I record with my digital recorder.

Even when I sync them up manually, for a good first few minutes, the streams from both the media playback in sync, but as time passes, the digitam camera playback starts to lag behind in both audio and video. The audio from the H1 Zoom outraces it.

How do I sync up sound (and video) from my video file from this digital camera with that of my audio file from the H1 Zoom?

I am listing the codecs of both the audio and video streams in both the media.

Properties of video recorded with my old digital camera
*Video Stream*
Codec: Motion JPEG Video (MJPG)
Frame rate: 29.970029
Decoded format: Planar 4:2:2 YUV full scale

*Audio Stream*
Codec: PCM MU-LAW (mlaw)
Sample rate: 11025 Hz
Bits per sample: 8

Properties of audio recorded using my H1 Zoom
File Format: WAV
Codec: PCM S24 LE (araw)
Sample rate: 48000 Hz
Bits per sample: 24


I am guessing it has to do with the higher bit rate of the latter. But how do I fix this?
You could try processing the audio first to get it to the same speed as the video playback. Using (for example) Audacity you can apply a speed change of -0.1% (1000/1001) which is very likely the amount you're drifting by. You can change the rate without changing pitch, but if you can tolerate the very slight pitch shift you'll get slightly better results by just changing speed.

If that isn't the correct rate, then you need to determine the change needed by measuring the exact length of the audio tracks between two points near the beginning and end. Once you know them you can compute the ratio and apply that.