You have misunderstood. They don't generally catch fire if abused as you describe. There is little or nothing to burn other than perhaps some dust inside it, or the laquer on the windings.
Automotive alternators are not designed to run at full output indefinitely. They don't catch fire if you run them at full chat for hours on end, they simply get so hot that diodes fail or soldered joints melt and they just stop charging.Permanently. You have clearly not run yours long enough to reach this point. Yet!
Just monitor the temp of your alternator and stop charging if you think it is it getting too hot. Use your 'engineering judgement'.
If you introduce a small resistance into the cable charging the LFP, you can limit the alternator output to a current low enough to prevent the alternator ever getting so hot it damages itself. This technique is (weirdly) dismissed as a bodge here, even though it works brilliantly.
This bit I really don't understand. If you are disconnecting your start battery from the alternator shortly after starting, its no great surprise it isn't getting charged.
Why not leave it connected to the alternator all the time, just like everyone else does?