I think you are off to a great start.
Your best bet is probably going to be to replace all the old equipment with new stuff as soon as you can. Since heat is critical, start with a thermostat and digital thermometer. And get some clean, fresh bedding! The UTH is probably good, they last a long time usually.
From there, ditch the heat lamp if you can and work on bringing up the humidity. If you want, you can get a digital humidity gauge, or if they have shops near you that sell pipes, cigars and such, get one designed for cigar humidors.
Once the heat and humidity is stable, then you can worry about changing prey size if needed.
Just take it slow and focus on one thing at a time so you don't overwhelm yourself.
Gale