Wasn't there some small turbofan/turbojet engine with dual centrifugal compressors (each in the 5-6 pressure ratio range adding one to the other to get a 10-11 pressure ratio range) available on sales a couple of years ago?It seems to me a low cost turbofan would be better off using twin centrifugal compressors (staged) rather than multiple axial stages. Way cheaper to machine and assemble and would get you to the 9-10 pressure ratio range. A geared fan would massively increase cost and complexity of design/manufacturing.
No problem to find CNC machines capable of machining nickel alloys. Ceramic tools can wail on Inconel or hard 17-4 at amazing rates, but that machine time will be expensive for sure. Luckily we're talking pretty small parts here for this thrust range so material costs and machining time is lots less than 5000 lb. class engines.
IMO, getting a design that works well and reliably with decent SFC and surge margins will be a lot harder than machining the parts for it.
The key to this whole project is the engine and that's going to be the hardest part too I think.
And what would be the losses compared to an axial compressor? Modern turbine engines seem to be losing 30% to 50% of power just to drive the compressor... For a scaled jet, such losses would be a major obstacle in achieving good performace.