Sounds great, except for the burning in the bottom and agar part

What I think you should do:

Turn down the heat when you are boiling, and stir the mix at all times (scraping the bottom) to avoid burning.. I don't know how burning it affects the medium but it might have a negative effect.

Regarding the agar two things:
From your description it seems that you forgot to boil the potato mash in only half of the water to start with (?) - Just to recap the recp: Boil the potatoes in half of the water for 5 mins (5 mins when boiling that is) !!and do remember to stir here!!. After these 5 mins you put in the honey water - bring to a boil again, and then add the agar.
In this way more of the water evaporates I guess, you could try or:

Simply add more agar - if it doesn't harden at all maybe twice the amount, if it's just soft jelly maybe you should use 6-7 grams instead.

Nice pics by the way!

Looking forward to your results,

Christian