leeneia, the movable bridge is probably a clever adaptation to either change key or adjust the tuning of each string because the range is very limited on a small number of strings.

This is how I assumed that a lyre would be mostly played:

A Trossingen saxon Lyre - 6th century being played by plucking the strings.

But looking at videos I saw a clever technique for chords:

Strumming technique on Trossingen lyre - Ar Mor Benjamin Simao

Both techniques

When I am tuning my Celtic harp I can tell when the string is reaching a critical state close to breaking point. I had a harp made by someone but I wasn't happy with the range of notes on it so I tried to change it up to a higher range but the strings were not happy so I had to stick with the original range. I bought fantasticlyu beautiful strings from Markwood Heavenly Strings & Kits and the problem was solved.

I think that if you tighten the strings - or as you said, there is only one string threaded in an out of all ten pins - to the point where the tension is tight but not too tight to be in danger of breaking and they resonate ok, then move the bridge carefully and check the tuning of each string. Hopefully the bridge can be moved at an angle so that all the strings are in tune in the range you want or possibly the range that the instrument will allow.

Having only one string might make it difficult to precisely adjust the tuning of each note. Question: do zithers have only one string. I vaguely remember hearing that. Their tuning arrangement is more complicated.

Another issue with playing a lyre, which is a similar issue that I've seen on the African kora, is that some of the practical technique revolves around holding the instrument but a harp stands on its own or is supported in the lap so both hands/all fingers can be used to create the music.

I'll be interested to find out how this works out for you. Please keep us posted.