Just take the filter media (part or all) out of the 1st filter and put it into the second filter...assuming that's possible with your filters. Your 1st filter will regrow bacteria just as it would when you replace media during maintenance. This will make your 2nd filter usable immediately.
Your idea of running both filters in the original tank will work too, but I'd give that 1-2 weeks.
I've used both methods and prefer moving the media because it's faster and easier.