Most animal poo is acid but some is worse than others, chicken manure is horrendous unless its matured for over a year.
I managed to get the tyres so high for 2 reasons I think;
1 PFA are very tall, slow growing spuds
2. I layer my compost in the tyres like this;
Thick cardboard (Wetted) only have the carboard in the first tyre.
3 or 4 inch layer of straw (soaked)
3 inches old spent compost
2 or 3 layers of newspaper (wetted and/or shredded)
1 or 2 good shovels full of well rotted horse manure
6 inches new compost or topsoil, soak really well then plant the tubers in this layer.
That should fill 1 tyre depth, just about. Then when the leaves grow above that I repeat the above mix. Remember the straw rots down quickly so the whole level settles down.
This mix isnt heavy so it doesnt squash the potato stems as just pure compost would. I also sometimes place a peice of wood over the tyre to darken them and force the shoots, but you must be really carefull doing this or the stems get too weak.
Every now and then I also add slug pellets.
I have done this with several varieties of potato and got great poundage of spuds and along the way I have converted most of my fellow allotmenteers to this way of growing them.
I also grow pumpkins and squashes in tyres full of well rotted horse manure.
Dig a hole about 6 or 8 inches down, put in several layers of wetted/shredded newspaper (these help retain water) place a tyre over the hole, fill with well rotted horse manure, make a mound of the topsoil you have removed on top so its higher than the tyre edge then plant your plant.
This has the added advantages of you always knowing where to water the crown of the plant and you dont waste manure by spreading it where you are not actually going to plant plus I get the best crop I have ever got.
Hope this helps
Jackie