I bought a 2500W champion generator last summer to run the AC in our travel trailer. Much like you, I hate generators with a passion.
The speed at which the batteries will charge depends on quite a few things, and there's no easy answer. Everything starts with the energy source, in this case that's the generator. If you have a 15a port, then you can't draw more than 15a (at 120v). If you have a 20a port, then you have even more room to play with. 15a at 120v is equivalent to 150a at 12v, which would theoretically allow you to go from 0 to 100% charge (in your 300a battery bank) in 2 hours. But that won't happen.
Your onboard charger/converter will typically be limited to around 45-55a. Look up the unit you have and you'll find its specs. The wiring in the trailer will also likely be sized for no more load than this, meaning that you can't even "easily" drop in a higher-power charger. Then there is the charge profile in the charger, which will limit how much output is sent, depending on the state of charge of the battery bank. The higher the level of charger in your batteries, the slower the charger will charge.
Some people install additional chargers to put more charge into the batteries at a quicker rate. I've seen numbers quoted as much as 70-80ah.
My trailer has a converter rated to 55a of output. When my 200ah battery bank is at about 70% or higher, the converter's charge map allows an output of only around 10ah. (I'm going off memory here, there are more precise figures in my build thread.) When discharged to 20% or so, it allows 40-50ah of output. This means that if I were to start with an almost fully discharged battery bank, the first few hours will charge it at nearly max capacity (of my charger/converter), but then it slows down quite a bit.
I have a 40a DC/DC charger that does put out a stable 40ah whenever my vehicle is running, so that charging method is easier to predict.