I'd think twice about putting spatterdock on any lake, while spatterdock is a waterlily subspecies it is a quite fast rambling plant, left a long time it will choke a pond and create a difficult problem long term, compared to hardy waterlilies and hybrids. Fortunately it seems you have them in a sheltered area which they havent been able to drift out of .
Its a bit like comparing daffodils, to dandelions.... The waterlilies have some great features for creating good shade and shelter for fish, though in their early days you may need to put mesh cages over the first crowns while they get up to speed and make numbers, ducks will try to chobble on the juvenile foliage early in the year
Large waterlilies you might take a shine to are: Gladstonnia, Richardsonii, Attraction, Rembrandt, Mayla, Sunrise, Sulphurea... Its a good idea to choose large waterlilies with good reputations for high flower to leaf ratios rather than 'whats cheap' if your priority includes wanting something to 'look good' as many water lilies have quite poor flower characteristics
As for cat tails, they are seriously invasive plants, worst characteristic is their thick strong tunneling rhisome... you could consider small forms of cat tail such as angustifolia or laxmanii, which won't present such a difficult problem to trim when they need thinning out.
Theres quite a lot of aquatic plants to improve the diversity of a lake or pond, when you start searching a few good varieties to start with, say, in a search engine like google, you will soon start locating plenty of good information and sources for interesting stuff that does what you want.
Regards, Andy
