Electronic – Maximum current draw from 12v sealed lead acid battery

Let's clear up some terminology first. An Amp is not a discrete quantity of energy. It is actually a quantity of electrons per time. Therefore, you don't say "Amps per hour". I like to use the analogy that Amps of current is like speed in your car. If you drove your car for an hour at 60mph (pardon my English unit assumption) and someone asked you about your drive, you wouldn't say "I drove 60mph per hour". That would be silly. Instead you would say "I drove 60mph for an hour."

It's the same with current. A battery doesn't supply 5 Amps per hour, it provides 5 Amps for an hour. Furthermore, a battery that has supplied 5 Amps for an hour has provided 5 Amp-hours (5Ah) of charge. An Amp-hour is an actual discrete quantity. It represents the capacity of the battery.

So you need a battery that can provide 5 Amps for 2 hours at 12V. That's 10 Amp-hours total. More specifically, since it's 12V: $$5A*2hours*12V = 120Wh$$
Of course, you would never want to buy a battery that can only provide exactly the capacity you need. You want some capacity in reserve. So let's double it and say you probably want a 240Wh battery. That way, you'll only use 50% of the capacity in one session.

The Li-ion battery you mentioned in your question has a 9800mAh capacity at 12V. That works out to 117.6Wh. Almost enough to last for two hours with a 5A current draw. As long as you understand what you're doing with a Li-ion battery, that should work, but I would recommend putting two in parallel to double the capacity. When you put two batteries in parallel, their voltage stays the same (12V) but the total capacity doubles (9800mAh * 2 = 19.6Ah).

EDIT: Looking at the website for that Li-ion battery, it is not clear what its continuous current capability is. It may not be able to supply 5A of current continuously without overheating. Without a datasheet or more technical specs, it's probably not safe to use.

One other note, batteries are not perfect energy sources. As you discharge them, their voltage lowers, their internal resistance increases, and their ability to supply current decreases. The more current you draw at a time, the more these negative effects occur. What all that means is a 10Ah battery may not actually supply a full 10Ah before the battery is flat. This is another reason to get a battery that has a larger capacity than the math dictates.

The short answer is - NO! No need to waste power from the panels.

You are correct, the lead acid batteries are best charged on a CC-CV logarithm. However, constant current doesn't mean that the battery has to be fed an exact pre-determined current or the battery suffers. It would be better interpreted as a maximum current that the battery can be charged at.

In an ideal world, where lead acid batteries worked better, we would just apply the voltage at the level of the constant voltage and let the current flow in until it saturated. Unfortunately, if we did that with lead acid batteries currently being produced, the current flow at lower charge levels would be so high that they would fry the battery. As a solution, the charge starts at a constant current level that is lower until the battery starts to fill up to the point where you can apply the constant voltage voltage and the current at that point won't be too high because the battery is already fairly full.

So if that made any sense, you should be fine to charge the lead acid battery at a lower and uneven current in the constant current stage of charging as long as the current doesn't exceed what the manufacturer recommends for the battery that you are using.

Specifically to answer your question, charging at lower current doesn't hurt the battery (unless the current is so low that the battery never charges because self discharge is greater than the charge current!).