Hi Leo ,
Did you try butting a 3rd box inside the -55 cooler box just a thought .
even though in theory its possible to cascade Peltier cooling and each level
will decrease in efficiency but adding a 3 level will give you hopefully another
minus 8 to 12 degrees maybe more 15. would be about max.
..
I did build a minus 80 cooler when I was working in Kinston for a company.
for testing equipment before sending to the Antarctica . . That was a very long time ago early 80's . It was done by converting an R12 freezer and changing the gas to 13B1 which was very expense and I believe it is now been band from use in the UK .
The freezer you are using is probably one of the new Green Gases . maybe
R161 which is basically butane or R404 or similar .
What I think you need is to get hold of a second hand lab freezers which
I believe use R508B and can go down to close to minus 80 .
I am retired now so I have lost track on the new refrigerants .
I would Try Cascading Peltier plates with an external power supply is certainly the cheapest way . You can sandwich Peltier plates but you need
a very good thermal grease between each and a thin copper sheet .
to help with thermal movement as they expand and contract the copper sheet will reduce the ceramic from cracking .with luck . and lots of Power amps.
Note ( Make sure the Peltier plates are orientated hot,cold,hot,cold )
placing 1 plate wrong it won't work . also the power has to be monitored
the first sage will use more than the second .
The first sage is the one within the -42 side (Edited due to Typo )
second as final or if 3 stages and so on .
I have only ever used 2 stages . as they become hard to mount .
A tension plate with springs should be used to hold them together