Overdosing doesn't do anything... trust me I have personally done this to my 3 main tanks.. I have a 55g, a 30g and 27g they all at one time had black beard hair algae on my plants... Even the bottle of excel says if you do a water change to add 1 capful PER 10 GALLONS.. that's 5-6 cap fulls for a 55g.. lol
for the 55g I would use 3-4 capful every single day and keep an eye on the algae garuntee itll turn red within 3-4 days, and when its red its dead. as for the syringe.. eh... black beard can be all over the tank a syringe doesn't really do much.
I once had hair algae ALL over my driftwood.. like I mean covering it you could see it sway in the current.. and once I used excel it died in a week or two and never came back