Bacon fat and plain oil browned just as well
Cooking in bacon fat or plain oil instead of lard consistently raised depth of browning to 7-8/10 across three reports.
Substituting oil, bacon fat, or a partial amount of reserved rendered fat for lard when crisping the meat still produces good browning (7-8/10) — the specific fat used matters less than the act of actively crisping.
This is the same pattern the rest of this family shows. The identity of what you pour in is close to free; the quantity and the level are what decide the result. What matters at the moment of the crisp is that there is hot fat and no water — and a fat is a fat for that purpose.
What to do: the fat the pork rendered is already in the pan. Skim it off the drained liquid and crisp in that. If you need more, use whatever is in the house.