Can I run a 110v battery charger/maintainer off a solar panel?
I would eliminate using the existing charger and inverter because that is inefficient and adds more complexity than is really necessary. 

The wattage of the panel really tells you how FAST you can charge the battery. That is, using a higher wattage panel will charge your battery faster in optimal sunlight conditions.
That being said, I don't know how fast you want to charge the battery, but I will give you some formulas that should help you choose what you really want.

The stored energy of a battery is usually measured in Amp Hours (AH). You can usually find this on the label of the battery. Except we are interested in the POWER that it can deliver. To convert Amp Hours (AH) to watts hours, use the following equation:

Energy = (AH) * V


Where P represents the STORED energy, in watt hours (WH), AH is the amp hour rating of the battery, and V is the voltage of the battery. Similarly, in a DC (Direct Current) circuit, the power delivered can also be calculated using the following equation:

P = V * I


With P representing power in watts, I the current in amps, and V being the voltage. It is not that hard, or expensive to build your own solar charger circuit using a regulator, a diode, and some other inexpensive components. Calculating the power of the charger is pretty simple as well. It is just the power coming in from the solar panels, minus the power dissipated by the components. Check out the link below to learn more about building a charger circuit:
http://www.electroschematics.com/6888/solar-battery-charger-circuit/

(Or you can always measure the output power of a charger by measuring the voltage and current coming out, and plugging those values into the equation above.)

Lastly, to find out how long it will take to charge, just do some simple mathematics with units. For example, to find how long it would take to charge a 12 volt, 40 Amp Hour Battery (like a car battery) with a 20w charger, you just do some unit conversions:

First, find the stored energy in the battery in watt hours: 

Energy = (40 AH) * (12v) = 480 WH


Then find the amount of time it would take the charger to completely charge the battery:

Charge Time = (480 WH) / (20w) = 24 Hours 


Note that the watts cancel out to leave you with hours for the time unit.

Hope this helps!