My girlfriend has a Fluval U2 and had, had the Stingray 15 that came with the Elite 60 tank. I managed to get the Stingray to cycle in my tank after some time but it did struggle at functioning properly, leaking through the case sucking up sand into the motor etc.
The U2 is perfect your tank and once you get it going you can really sit back and relax. If you want to transfer some media when you get the Fluval U2 (if you decide to) you will want to obviously transfer some media if not all of the media to your U2 from the Stingray Filter.
The best method I can think of at the moment for this would be to take the 2 sponges from the stingray the pyramid shaped one and the Pentagon shaped one. Then slice the Pentagon one directly down the middle and the triangle one into about 4 wafer thing slithers. You can then place one pentagon shaped sponge in either side in place of the Poly/Carbon insert and then use the slithers from the pyramid shaped one to fill in the gaps. Trim off around the edges to make it fit into the basket/case/slide properly. This will all make sense when/if you get the filter (Though I do highly recommend it over the Stingray 15).
You can do this a number of ways however the best I can think of is removing the Poly/Carbon insert from the fluval U2 and replacing it with your Stingray foam as stated above, or you can always cram it inbetween. However it probably wouldn't be best to do that. I find the stingray foam clogs up too easily to be placed as the first sponge on the Fluval U2, it's not well shaped enough to be the main "dirt collector" either and you would probably end up with a lot of leaf/poop/general gunk in your impeller if you were to replace the outer sponge. Though I do recommend you replace the Poly/Carbon sponge with your stingray sponges.
Further more it is always handy to have the PolyCarbon inserts kept at the side for a future date incase you have to medicate the tank. The mistake I made was cycling the tank with the Poly/Carbon in the tank and then realising the Poly/Carbon is a fantastic surface for bacteria to cling to.... Unfortunately If I need to medicate the tank i would be removing a huge amount of bacteria and then not only be treating the tank for a disease but also for a probably ammonia/nitrite spike.
Anyway Good Luck, I've felt exactly the same as you when it came to that tank!
P.S, Can only reduce Nitrates via Nitra-zorb I think... Plants... or water changes (preferred). Though I would wait to see what someone else says about that!
Also test your tap water, you may find you actually have very high Nitrate in your tap water. Though having 0 Ammonia and 0 Nitrite whilst doing a "Fish-In" cycle sounds to me that you aren't actually "Cycling" anymore and in fact "Cycled" for your current fish load. However only time will tell and I would advise not adding any more fish until you have made the transfer to the new filter properly. It may cause a little disturbance but if enough of the bacteria is transferred the filter will pick it up fast. The FLuval U2 has 5X turn over in an hour for the Elite 60. However that is of course going off manufacturers claims so it will probably be about 3x. I think the FLuval U3 would be a very unneccessary overkill for the elite 60 and I'm not too sure but may actually take the entire room from the substrate to the top.
Furthermore! Another edit yes in the space of 2 minutes another one!!!
I have found having a very fine layer of filter floss before the ceramics (between foam and Poly/Carbon)is EXTREMELY effective. There is massive noticeable sized colonies and it does NOT effect the flow of water at all. It is also great for transferring media to a friend or another tank without harming yours. I in fact seeded my filter off my girlfriends by removing some ceramics and filter floss and within 2 weeks my tank was fully cycled. Though 2 weeks later I still haven't decided when I want to put fish in haha.