I eat a lot of mostly grass-fed beef. I eat a lot of eggs. I've been considering storing the tallow left over from frying my beef and using it instead of butter to fry my eggs.
My main concern with this is that the second heating of the beef tallow may mean a second chance for it to be negatively affected by the heat and degenerate into toxic compounds. Additionally, since I often cook multiple batches of beef in the same meal in sequence, using the tallow on the eggs could mean some of the oil has been heated four times already. I don't think I go over the smoke point when I cook my beef. Do animal fats need to reach their smoke points to degenerate into toxic compounds? Is re-heating beef tallow multiple times a bad decision? Or should I get fresh tallow to apply to the pan each time?
Tallow has a smoke point of around 420 F, so I'm pretty sure you're correct in thinking that you've kept it well below the smoke point. (No harm in using a thermometer next time to see how hot it gets, though!) And yes, tallow (and fat in general) needs to reach its smoke point (or achieve very very very slow oxidation at room temperature) to be toxic. However, the next time you use fat that's already been heated, its smoke point will be lower than it was before. How much lower, I don't know, as it's correlated to how high it was heated to when it was rendered, but it's something to keep in mind. I'd be wary of using tallow that you think has already been heated to high temperatures 4 times, but if I understand your process, then you could pour off the fat (into a filter over a jar or bowl) before you start a new batch of beef to cook, right?
In any case, I think you should be perfectly fine using filtered tallow rendered from frying beef for one more use (provided it doesn't look or smell rancid, obviously).
I've found variability in how well my tallow holds up, highly correlated to whether it's from healthy cows or not, strangely, but it could also relate to how hot I've rendered it, with too hot or too low being problematic. I would say to try reusing it, but if it smells or tastes bad, throw it out.
Another option is to mix it into your food after you cook it, so that you don't have any fat leftover, depending on your fat intake goals.