The S2+ has best genes for a cheap flooder. It has no wide head for a useless big reflector and it is budget but solid. Modifying one of your S2+ is the cheapest way to test what beam angle you finally want. (A too large angle might give you too little light intensity or too little runtime outside.) Just test it.
For a very wide angle of 80° a Carclo 10170 reflector would be the best choice - but you need an account at Mouser, Digikey or any other specialized sellers to buy them. Or you could by some other stuff from Kiriba-ru and get one free 
Ledil C13353 LEILA is a similar reflector with a slightly smaller beam angle.
The reflector of the S2+ has a diameter of 20.4 mm and an overall height of 11.6 mm. Anything around that diameter and below that length may fit (or you can make it fit).
You could try one of the Aluminum Orange Peel Reflectors at Fasttech but I doubt they have a wide beam angle.
A popular choice for different beam angles on the S2+ are TIR optics. Fasttech’s 21.2*12.6mm PMMA Lens for Cree XM-L will directly fit into a S2+. It has 60° and there are other (narrower) beams available. Details and screenshots here.
Fasttech’s 90 Degree Optical Condenser Lens will need some rework because it is too wide (22 mm) and too long (14 mm). Most other very wide angle TIR optics are quite short (around 9 to 10 mm), like the 80-degree Lens. I have not tried it but taking a few threads away from the front of the pill and using a spacer against the battery may do the job.
And finally you could make a Mule - no optics at all. Just position the emitter directly behind the lens on a long heatsink against the pill like it is done on most S2+ Triples. The Cree XM-L2 LED has a beam angle of 125° but you may lose something from the total reflections at the lens if you want one.
Oh, I forgot: There is a diffuser available for the S2+. Review is here. I will definitely try it.