Try to make a prediction on how you are going to use the bike. All freeway driving won't be a problem. All city driving might be. Project how long you expect to operate below 2000 RPM, or what percentage of key switch on time. At idle speed, the alternator makes about 1/3 of full output, about 50W at 1000 RPM for the 550 which is 4 or 4.5 amps.
Remember, a battery ought to have at least 12.6 V. Higher voltage means the alternator is keeping the battery from depleting. Lower voltage means the battery IS depleting.
Be aware that the Dyna-s almost doubles the coil's power consumption. If you are aiming for efficiency, the Dyna-s will not provide that and works at cross purposes to having a smaller capacity battery.
Most 550s, suck about 10 Amps when key switch and lighting are on. Yours will draw about an amp more than a normal 550.
Battery ratings are made at a 10 hours depletion rate. A 4Ah battery will keep above 10V with a 0.4A drain over 10 hours. Increasing the load drastically shortens the capacity. You will not get 0.8A out of that same battery for 5 hours, for example. It is probably more like 2 hrs. for this example. And higher discharge rates make for faster depletion. It's all about chemistry and chemical conversions take time to complete.
Also note that the recharge rate should be limited, to lessen battery "fatigue". A safe charge is about 1/10 C where C is the discharge rating. Yes, you can stuff 4 amps into it to recharge when depleted, but the battery won't reach full capacity without overheating it. A 4Ah batter should be charged at 0.4A to safely make it reach full capacity. The bikes regulator will not not care about this.
One strategy would be to buy two small batteries and change them daily, putting the alternate day battery on the battery tender to restore it to peak.
What price style?
