Oven won't light unless it's hot -- but it can clean!
As others have suggested, the first thing to check is that all your valves are fully open.

However, since you don't seem to be having trouble getting up to temperature, it seems less like a supply or regulator problem and more likely to be about location of the pilot / ignition source.  Either it's not clean, or position relative to the gas is off (could be not enough gas, or not enough supply air).  Make sure your stove is level. If that doesn't help, see if you can clean/replace or adjust it.

A good generic step by step troubleshooting guide can be found here, which lists the order of trouble shooting for a milivolt ignition (the kind of pilot you hear clicks) with as: 


The gas valve
The thermostat
Cleaning the pilot orifice and pilot generator
Adjusting the pilot generator height
Replacing the pilot generator and safety valve