Assuming you are going from stock batteries, you had 160 to 200 AH of lead acid on the trailer before. Going to 220 AH is not going to change things much. If you toasted the old batteries by running them down, you probably will toast the new ones as well. Ten or twenty percent more power just isn't enough to change the way things work.
Going up to 300 AH is a boost over what you had. Keep in mind that with lead acid, you only get half the capacity number as usable amp hours. The "stop using" point at 70 F is 12.2V on most of them. If it's cold outside, that point may be up around 12.8V. Go past that and the battery wears out quickly.
With 150 AH *usable* (and a 100% charge to start) with no solar you get 30AH a day for 5 days. That's an average load of just over 1A ... good luck ....
With 200W of solar in the sun, you should get 10 to 12A of charge current. If you get it for an effective 8 hours a day that's 80 to 96 AH. You are running lead acid's so about 20% of that vanishes in the lead acid chemistry. Net is a charge of 64 to 77 AH per day. If you run big loads during the day that would change a bit.
So, if you can stay inside a roughly 70 AH per day budget and live in the sun, you can go on forever and ever. Of course that was also true with your old batteries and they didn't make it.
So what have you gained? On a 5 day trip in the sun, your old power budget was 70 AH. Your new budget is 70 + 30 = 100 AH. Like any budget, in order to keep to it, you need to be able to track what you are doing. A shunt based battery monitor is the key to doing that. If you are already tearing out the batteries .... might as well toss one in.
Another cute device to think about is a battery cutoff device. It monitors the battery voltage for you and shuts off all the loads when you hit the magic voltage. They aren't terribly expensive. Way cheaper than a new set of batteries
So, could you upgrade your solar controller? What did the dealer put in already ? No matter what he used, there is probably something out there for more money that is in some way better. So yes, you could upgrade it. Will it keep your batteries from frying? Probably not. Only proper monitoring and shutting things down will do that. Sorry about that.....
Of course you could go for the same amount of weight in lithiums .....