But the big challenge for SpaceX now isn't one with astounding demonstrations of technology. It's doing the same thing over, and over, and doing it quickly, and making a profit.
I agree with you that is a core problem for the company. Having two launch pads in Florida and getting the third launch pad in Texas (not ignoring the one in California.... but that is specialized for polar/military payloads) is going to help a lot in terms of clearing their manifest too. Gwynne Shotwell just gave a speech with a Q&A recently about the Falcon Heavy and made a few remarks about the work done on pad 39A too. They are just about ready to start using that site for launch operations there, where a second launch team is likely to help increase that flight rate.
I'll also point out that at the moment range operations at Cape Canaveral in general needs to be streamlined if launch rates are to be increased. That involves more than just SpaceX and might even require a general rethinking for flight operations there for the other launch providers that use the same site. I know for a fact that the Space Shuttle really messed up launch schedules where a Shuttle launch not only took priority but also blocked out a huge hunk of the calendar for nearly a 3-4 week period of time. I would expect that the SLS and the crewed launches (both SpaceX and Boeing are launching out of KSC) are going to be in a similar situation.
By Texas law and the contract signed by SpaceX with the City of Brownsville and the surrounding communities, the Brownsville spaceport can have at most 12 launches per year and each one must be no closer than 20 days from the previous launch. While that might help work around some scheduling problems for some payloads when stuff is happening at the cape, it doesn't mean there is going to be much more of an increased launch tempo.
In other words, I think about the most that almost any private commercial launch provider could ever do right now with the current launch infrastructure for orbital spaceflight in America is about 20 launches per year... and that is being very generous. Last year SpaceX got in seven flight, with one catastrophic failure that required a full engineering review and a return to flight program that satisfied not only the FAA-AST regulators but also all of the customers... especially NASA and the DOD. If they get over a dozen flights in this year, I would be surprised.