Once the deposits form they're virtually impossible to remove by flushing, so changing coolant now won't have any effect. You should start shopping for a radiator. It's probably made by Behr and available through the aftermarket, which might be cheaper than the dealer.
I believe there are also some outfits that can remove the plastic side tanks, which would allow the core to be "rodded out", and then install new tanks.
Your starting problems are unclear. Is it hard to cold start in hot weather, cold weather - hard to start after a hot soak, what? Be more descriptive of the conditions where it starts easy and starts hard. Electrons are cheap!