Ok, I don't have the benefit of actually having tried any of this, as my capacitors still haven't arrived. But the reason red LEDs aren't much good is a typical red one will start conducting at about 1.7 volts and less than 1 milliamp, which is negligible for this purpose. At 2.1 volts it's around 10-15 mA. You could pad it with a Schottky diode, but the forward drop is load-dependent and it would be hard to know what you were getting. A white/blue LED is on about 50 microamps at 2.7 volts, so that's no good. Whether or not the red one does the job, it will deplete the charge over time, or not work at all. I can't know any more until the capacitors arrive.
The 7.5Ah LiFePo4 battery has arrived and I have installed it in the car.
I had to pack it with a big chunk of wood and some foam pieces to keep it in place. It weighs almost nothing, makes you wonder how it can work.
I left the original battery terminals on, just in case I want to revert. I'm not planning on it.
The first thing I noticed is the starter cranks over noticeably faster than it did with the old battery. Since I only bought the car 8 months ago, I have no idea what is the condition of the battery. A good test is to put the roof up and down without the engine running. The hydraulics puts a pretty heavy drain on the battery, and it had begun intermittently failing partway through the cycle.
With the new battery, the roof zips up and down no trouble at all. So, I'm impressed. This is just a motorcycle battery, after all, not meant to be putting in cars. Looks like I don't really need the capacitors, but I will put them in anyway. It has to make life easier for the battery, I think. I will update when they arrive.