Brazing is generally a good way to repair cast iron but it tends not to be very easy to fill large gaps. You certainly can braze with a sufficiently powerful venturi burner using propane only but if you want to build up metal you will need the more precise flame that you get from oxy/gas.
Oxy/propane will certainly work and propane is much less dangerous to store than acetylene.
Stick welding can be successful for repairing cast iron, generally nickel electrodes are used, brass electrodes don't exist but you can get bronze ones which should work. However you will probably still need to pre-heat the work to reduce the risk of cracking.
Another alternative, which is quite attractive if you don't need high temperature resistance is to use a metal filled resin. You can make this up yourself from eg epoxy casting resin and fine brass powder. This has the advantage that you don't have the thermal stresses which are what cause the problems in welding or brazing cast iron.
There are also techniques which involve cutting keyed slots into cast iron and peening in cold metal slugs (usually nickel) but this is more for crack repair and may not be suitable for this application.