I have never used mother cultures, but everything that I have read advises against it for the home cheesemaker. The main concerns are around contamination and consistency, with such cultures tending to change in composition over time.
There are some surface ripening cultures, such as B Linens, P Candidum and P Roquefortii which can be successfully grown from a sample of commercial cheese. You need to consider though, that these are salt tolerant, whereas the ripening cultures which you want to extract from your cheddar are not. That is why the cheddar was salted during manufacture: to stop the culture from working.
The culture which you have extracted from the cheddar may look promising but what organisms are in there? For starters, pasteurisation does not kill off all of the organisms in the milk, otherwise it would never go off.
Sorry to be a wet blanket. Your culture may work but it's not a risk I'd take.