Dividing tulips

I have a small bed where I planted 5 Tulipa 'Apeldoorn' about 9 years ago. I do nothing to them, and every year they return and increase: 30 or 40 blooms now. For the past 3 years or so I've thought they must be very congested and I should split them, but have hesitated as they do so well! But this year, while still looking very gealthy, the flowers were smaller so I really think I have to do it now. It's going to be a big job as I planted very deep!
I read that I should wait until the leaves had completely died back, which they have. But I can't decide whether to replant straight away (I want to put some back, and put others elsewhere in the garden) or store them and plant in autumn. I'd prefer to replant immediately, but am paralysed by indecision.
What would you do?

 

I'd get on and move them around now. I'd also replant the ones I wanted straight away and maybe give them some blood, fish and bone.
Then maybe after flowering next year give the bulbs a feed.
When you come to dig them up they might not be at the depth you planted them as bulbs have a tendency to move around to where they "feel" comfortable.

 

Thank you @NigelJ . I will do that (minus the BFB as I can't use anything like that without foxes causing chaos!)

 

Tomato food might be another option @LG_ but I'm not sure whether it might be too late as they will probably be going into dormancy now.

 

Today was the first chance I got to dig them up. I found 30 full-sized bulbs, about 40 smaller but substantial ones, and about 60 or 70 'babies'. All firm and healthy looking (except the 3 I put my fork through...). Not bad for having planted 5 bulbs to start with! I wouldn't be at all surprised if there are still some underground.

I had planned to replant straight away but don't have enough time/energy to sort that out today so I've bagged them up in the shed. I'll probably replant all the big ones and then think about potting up the others to let them grow on to maturity... Not sure where though!