Sounds like you want to remix the individual tracks, to get a balance of volume levels more to your liking.
There are multiple ways to skin this cat.
Old School - get hold of an analog mixer having at least 8 channels and patch the 1/4" outputs of your Blackface or XT ADAT to tge mixer. Play the tape and mix away. When you are happy with the levels, patch the stereo master out from the mixer to the stereo mic line in on your computer sound card. Record to a wave file on any DAW. Audacity is a free one. CD resolution is 44.1/16 bit if you intend the CD format. If you intend streaming you can select higher bit rates.
New School - have a transfer service extract the 8 individual tracks of each song and deliver them to you on a data disk or perhaps a USB thumb drive or cloud download.
Put them on your computer and mix the songs "in the box". As before when you are happy with the mixes, render them to your preferred format according to how you want to make them available.
CD, thumb drive, streaming platforms like SoundCloud, YouTube, bandcamp, Facebook etc.
ADAT tapes were at one time a professional standard, but that time has passed by for the most part.
Don't wait on this .The magnetic tapes degrade and the ADAT mechanisms wear down and develop flaws.
Get your tracks transfered to the current digital media.
Best of luck.