Since I am not afraid of competition

We pack columns with Haskel air-driven pump at constant pressure. This pressure depends on few things but the main one is the mechanical stability of the silica gel (or other particles). A typical packing pressure is 400-500 bar, unless you pack particles with big pores, then it is dropped to 300 bar, or even 250. Haskel pumps, in our packing stations, have a ratio 1:30 to 1:120 and our compressor is set 120 psi (10 bar) (so in theory you can create about 10,000 psi). if you don't have an air-driven pump, then you can use a regular HPLC pump which can deliver/work with 400-500 psi at certain flow rate (we packed our first columns with Knauer high pressure pump). The key top successful packing is to find right slurry (solvent in which silica is suspended) and pusher. Simple sedimentation studies can give you a rough idea what to use. After you pack couple of hundred columns you will know how to modify conditions to troubleshoot low plate count and poor symmetry.
Let me know if you have other questions. Good luck.
P.S. The fact that you don't have homogeneous bed tells me that you choice of slurry and pusher are not correct and that you are not passing enough pusher through your column.