I would say the first thing is to find out what you have for solar pannels.
I have seen 35 watt and 55 watt about the same size pannels with different designs. WidthX length probably is not a good way to guess at them. 10X35watt=350watts or 10x55watt=550watts, big difference in how much power your getting. Same basic length and width.
Since the system is already there now does not mean it was correct when built either.
I would start by trying to figure out how much power is made. To to find out what the pannels are etc..
In the first post,
"It seems to me that the obvious area that my system is lacking is in sufficient power battery storage. Since the sun shines nearly every day and I have 10 solar panels (not sure of their power capabality, but they are appx 1m x 0.5m each). "
Ok as I mentioned above, need to know how much power is being made to know how much is available to store in the first place.
I did not see a mention of how much power you use either.
Of course if you use 100amps and the pannels only produce 90amps, you have a problem of not enough power being made. Upgrading the batteries here will not help though because you would be using more than is made and would still have the same problem.
It is better to not mix new and old batteries, so if you upgrade your battery bank it's best to start with all new matching batteries. If you do this, then what you have now does not matter anyway, it still falls back onto how much power the pannels make and how much you use.
Testing the capacity like others have mentioned already is good and you should do that also. I just did not see your reason posted for WHY you think the batteries are the problem really.
In other words just because it's a bright sunny day and you have alot of pannels does not mean you are making as much power as being used. You need to measure your useage also.