I am on a poor internet signal, so I'll type here on your battery voltages etc.
Here is a chart for lead acid battery voltages when the battery is at rest. This is from the Trojan battery support website and what I use for how charged a 12-volt battery is.
See here on their website for more info; the chart above is from their older site https://www.trojanbattery.com/resour...ry-maintenance
NOTE: The voltages above are for a battery at rest, not on a charger or just off a charger. I check my battery voltage level while boon-docking first thing in the morning. While tiny loads are going on, I know it has bled down from charging voltage as at least 8 hours of low battery use has passed.
They use the term "surface charge" for the higher voltage that comes from charging a battery when the battery comes off a charger. That surface charge is not a good indicator of the state of charge; it must bleed off the surface charge after enough time to reach the true resting voltage.
Now to this comment, you said.
While it is running, the battery volts (read at the battery as viewed on our 30-amp solar charger), will reach a maximum of 13.5 v after about 4hours of run-time. When the generator is powered off the battery volt reading will drop to 12.9v. By morning the volts will be down to 12.6 (+/- .1). The first few days the first battery we tried would drop down to around the 11.2v but it was from 2018, so figured it might not be sufficient. We purchased a new Everstart Max marine Deep Cell Type 29DC battery from Walmart (that was the same size of the previous battery).
OK, now you have entered the words Solar charger, to sort out what the converter is doing, you need to make sure the solar system is not trying to charge the battery at the same time your old power converter is. Does your solar system have a unhook mode to not charge? and I'm assuming you are still on your old power converter that may not be working right.
The point is, if the solar if pumping voltage into the battery at the same time the old power converter is, the old power converter "might" get tricked into thinking the battery is charged enough. Let's talk about the power converter only and the lead acid battery.
There are 3 voltages used on lead acid battery charging, and your old power converter may not have all 3.
13.25 volts = float mode. The battery is at 100% state of charge (SOC) and only needs a very little amperage and enough voltage to maintain it, not charge it. This is float mode.
13.6 volt - standard charge. This is the standard charging voltage for a 12-volt battery. It raises the voltage high enough to charge the battery; the amperage will vary by the algorithm that your converter uses compared to the battery's resistance.
14.4 volts, this is boost mode, modern better power converters boost the voltage to 14.4 area to fast charge the battery up to 90% SOC then taper into standard charge, 13.65, and once at 100% SOC, the converter tapers down to float mode, 13.25 volt at very little current.
The voltage numbers above are a range of voltage, not exact. 13.2 or 13.1 are the same float voltage etc. as is standard charge and boost.
When you say 13.5 volts, that voltage is the standard charge voltage, but since you have solar in the mix, I have no idea if the solar is providing it or the power converter. But it is the charge voltage.
Then turning off the genny, the voltage drifts down to 12.9 volts. Yes, it will drop; the surface charge is bleeding off
You said the voltage tapered down to 12.6 volts by morning, which is now close to the resting voltage, which is darn near 90% SOC. The surface charge is all gone.
Why did I not get to 100% SOC? which is 12.7? Going from 90% to 100% takes a long time; think overnight charging or even two days to jam that last 10% into the battery. This is not going to happen off of normal campground genny run times. The best most of us get is charged to 90% SOC and maybe a little over as we have restricted genny run hours. In the places we camp, we can only get 5 hours a day genny run time . I have to be plugged into shore power for a day or two to get my 2, grp 27's up to 100%
If you want to test the converter, unhook the solar, plug into shore power or the genny, and use a volt meter right on the battery terminals and see what voltage you get,. It should be at least 13.6 range if the battery is below the high 90's in SOC. If you ever see 13.25, then it is in float mode, and it thinks the battery is charged to 100%. If you are on an older converter, they normally do not have 14.4 boost.
If your converter is dead or going bad, you can see low or mega-high volts. Both are bad news.
Amperage and how to read it, by using an amp meter or some sort, is about the only way other than one of these new super smart battery monitor units, which use a shunt at the battery to measure the amperage and give it to you.
I use a DC clamp on amp meter. Mine is a higher-cost one I had when I was working. I clamp the meter over the outside of the cable and read the meter. I can tell how the amps flow in or out of the battery.
They have many AC/DC clamp-on meters that are dirt cheap now, think $45 worth. The accuracy could be better, and the warranty, but they do work to help teach you what is going on. If you are interested, I can hunt up then one a fellow Sunline buddy just bought off of Amazon and link it.
OK, with all that above, read it over and report back to filling missing parts or more questions.
Also, a few battery health and maintenance health tidbits
1. When storing the camper, unhook the battery negative to not drain it dead with the parasitic loads in the camper. Or install a battery disconnect switch
2. For good practice, only draw down a lead acid battery boon-docking to 50% SOC as your low limit. The battery gets longer life when only going from down to 50% and then back up again. The battery gets less heat in it (which hurts it), charging up from 50%, then when drained down way below 50%. You do not have to wait until 50% to recharge; try not to go below 50% repeatably
3. For the best long life when the camper is not in use, get a battery maintainer with de-sulfate mode to keep the battery at 100% SOC. I use this one. https://www.batteryminders.com/1510-...-with-warranty
. You can buy them cheaper at other retailers. Northern Tool, Amazon etc.
4. If your power converter is old, consider an upgrade that includes 3-stage charging with de-sulfate mode. I prefer the Progressive Dynamics brand, but there are other good ones too. Here is where I buy all my power converters of almost any brand. Randy knows what he is doing and will give you good support. https://www.bestconverter.com/
5. The older power converters are nick-named battery killers, pending brand. If they have no float mode, they cook/boil the battery out over time, staying in standard charge all the time.
Hope this helps