There are a number of issues here.

Regarding a solution though.

What are the patches you are trying to load
They may already exist as a MIDI sysex dump.
This is in my experience easier to deal with.
Especially as I converted everything I could find and kept track of the legacy hardware and software to make sure I still had access.

If you have a sequencer package capable of sysex dump and the MIDI hardware, there's a solution
Assuming the Matrix 6 is functioning in this respect and you have MIDI cables.


Now the explanation of cassette dump issues.

The original system was designed around current technology and hardware.

A good working solution was to buy a Radio Shack mono machine and a pair of 3.5mm mono jumper cables.
It worked every time.

By the time I met this issue, in the UK, the cassette machine was not available.
I made an AIWA recording walkman work with a pair of cables I made.
The issue I found with this was fixed by recording both tracks and then picking one for replay, by the wiring inside the 3.5mm stereo plugs at the AIWA end. Labelled the cables so they always ended up in the same signal path
No DOLBY!

When the AIWA and the spare AIWA died, I tackled the problem with a
SONY Pro walkman, which had a line in, an essential part or recording the patch dump.
I used the headphone out as the line out didn't work well enough.
I standardised the cable, always using the same pair in the same signal path.
This worked great, and replayed factory cassettes from all known Obies, Sequential,Linn etc.
I could DOLBY B the record but replay without and it still worked.
Once or twice there were old cassettes that replayed at such a low level that there were problems.

An OTARI time code reshaper was used to basically clip and boost the signal.

More recently, I have replayed my cassette archive with a MARANTZ PMD520, with a Stereo 1/4in jack to RCA to mono 3.5mm adaptor, one channel only, and it worked on the Matrix 6.

Your method of using a wav file from a soundcard involves a number of possible sources of error.
Any phase shift at high frequency will modify the data returning from the wav file.
Most eq has phase shift effects.

It might be that there is an inversion of te waveform, not noticable on audio, but the Data won't be on the top edge any more, where the Matrix 6 is "looking"

It may be that the level is the main issue, you could try the headphone out if it offers one.

I have made wav dumps from a Toshiba laptop, which has a poor sounding soundcard compared to the G5, but I still have my  custom cables of proven functionality.