There was a method patented in 1896 whose claims would seem to meet your requirements. Even with your restricted budget, used laboratory equipment companies can probably provide you what you need.
An excerpt from the patent states:
"My invention relates to the production of graphite from any of the
cheap and common forms of carbonaceous materials, such as mineral
coal, coke, charcoal, gas-carbon, and carbids and the like; and it has
for its object to provide a process or method of cheaply and
practically producing pure graphite..."
The reagents used are common, cheap and readily available. The patent states that:
"[the mixture is] composed of powdered coke, sand, salt, and sawdust,
the coke forming about fifty per cent., by weight, of the mixture, and
these materials are thoroughly mixed and introduced into the electric
The key issue for you will be designing the high-temperature inductively heated furnace, though the patent describes this thoroughly, including diagrams.
The availability of used equipment to fashion the device as stated is of course uncertain, and you will have to be creative with what is available. I would start my search with LabX, with whom I have no affiliation whatsoever. I hope this does "point you in the right direction", and Good luck!