You will be fine, just pay the fine and take it as a lesson to be more prepared next time …(request your docs more advanced !!). Overstaying by a couple days is very common and as long as you’re not arrested on overstay, then it’s fine. Obviously don’t overstay as a habit but it won’t have any impact on your future in Thailand.
From my experience 100k in Thai gfs bank and sponsorship letter from me saying I would cover accommodation/food was enough to get the visa. The main thing to prove is that your gf has sufficient ties to TH that would ensure she will return at the end of the trip. House, job, dependents are all positives that would work in her favour.
I got rejected on my last online report (and told to go to report in person) but before I went in I resubmitted it online just to try it and I got accepted the same day 🤷🏼♂️