Maybe you could try to modify your PSs and link them to a substrate (such as gold or ..), then form a monolayer of PC on top of it. It may difficult to get a full monolayer of PS.
If there were an enzyme that could convert the serine head group of PS (-O-CH2-CH-(NH3+)COO-) into the choline head group of PC (-O-CH2-CH2-NH3+), you could make sealed, unilamellar liposomes of PS (if that works), then treat them to turn the outer leaflet from PS to PC.
Amazingly there is an enzyme, phosphatidylserine synthase 1, that catalyzes the opposite reaction, converting phosphatidylcholine + serine to phosphatidylserine + choline. Perhaps it can be made to run the reverse reaction. Or, start with sealed, unilamellar PC liposomes and convert the outer leaflet to PS.
Langmuir-Schaefer dips are rather straightforward to perform, although you need very precise equipment that might be very difficult to obtain (there's one at the PSCM, Grenoble, which I have used myself) and I guess this is the only technique that can really achieve asymmetric supported bilayers. However, your lipid composition (100% PS) can be tricky, and you may try to play around with pH and ionic strength for it to possibly work. Also, I'm not sure how long your membrane will really stay asymmetric (as stated above), as lipids can flip between the leaflets even without assisting enzymes. In theory one could try to use an electrochemical cell to stabilize the asymmetry (and there are people also working on such systems), but getting a completely asymmetric system with just PC on one side and PS on the other is probably impossible.