If I had to guess, these tapes were probably made on the Revox B-77, this is an excellent reel-to-reel which we used all the time in the studio I worked in back in the early 80's. You're going to need to find another reel-to-reel to transfer the tapes, however, beware of the following things!
1) Alignment of the heads. Reel-to-reel tape recorders as well as their bigger multi-track recorders are much more picky about head alignment than cassette decks. Make sure you align the head to the tape. Ultimately the best way to do this is with an alignment tape, but you can also do it by ear. Put a tape on, play it back and inside the head mechanism is a screw. Turn it until you get the best sound out of the tape. This won't be perfect alignment, but will put you in the ball park.
2) The tape! There was a big issue with all reel-to-reel tape made from the mid 1970 to the early part of the 80's. Playing most Agfa and Ampex tapes (two of the more popular brands used during this time period) with taking special precautions will result in a big wad of goo or simply watching the tape shed all the magnetic substrate as it passes over the pinch rollers and head and thus no recording at all. A special baking technique was developed which gives you a single shot at taking that material off the tape onto another material.
3) bias. Reel-to-Reel recorders are much more picky about bias when it come to tape. This is more of a recording to tape thing, but still nice to have set properly to maximize the audio frequencies. This should be done by somebody with the proper equipment and knowledge.
Wayne