It is true that the most receptive socialisation window closes around the 12-14 week period, but socialisation actually continues right through the juvenile period and as long as you are consistent and gentle in supporting her interactions with other people she should come round eventually.
I also have a 16 week old rescue pup who had his vaccinations delayed. We carried him absolutely everywhere we could for weeks - which was no mean feat as he's a lurcher and not exactly compact - and he's fine with buses, lorries, children, pushchairs, wheelchairs, walking sticks, umbrellas, loud-speaker system, skateboards, horses, cows, ducks - just about everything in fact, except other dogs. There was nothing we could do about it, we simply don't know anybody locally who has, fully vaccinated, nice well-balanced adult dogs we could socialise him with while we waited for the all clear and his jabs to be completed.
It's obviously easier to lay down good foundations and it's true that remedial training is often slower and a bit less linear than intial/primary training, but that doesn't mean it won't work - just that it takes a little longer. To be honest it's part and parcel of taking on a rescue dog and your efforts will be rewarded many, many times over.
My boy has only been allowed out since last Wednesday and I was really worried. The first dog he met was a teeny Cockerpoo puppy about a third of his size and he was petrified of it, but I have taken him to the park several times a day, every day, just for short periods and he's gradually been able to meet individual dogs gently on his terms as the days have gone on. Up until yesterday he was still backing up and refusing treats when a dog approached him, but today we have been to a country park and he's actually approached several dogs himself for a gentle sniff and hello and sat calmly with me outside the adventure playground watching the world go by and stuffing his face with chicken treats.
The important thing is to work at her pace and never push her or try to persuade her to interact with anyone or anything unless she's happy to do so. If she seems worried and backs off, let her, then when she reaches a distance she's comfortable with, let her just observe the scene and treat/reward her for being calm and interested. You should find, if you do this often enough, she will gradually reduce the distance she's comfortable with.
Last week in the park my boy was trying to bolt at the first sign of a dog approaching, so I let him lead me to where he was comfortable, then crouched down with him between my knees so he felt safe and we watched the other dogs together with me rewarding and treating him for staying calm. It's amazing how quickly he's come round.
You are in a slightly better position if anything, as you can ask people to be calm and gentle around your pup and they can offer her some of her favourite treats if she's happy to take them. If she doesn't feel comfortable with close up interaction, you could get them to just toss a treat or two in her direction while completely ignoring her.
If I were you I would orchestrate as many situations as you can where she can be around, but not necessarily have to interact with people in the first instance and build up from there. I know you said you are rural, but if you could perhaps go to a local village and sit on a bench with her, feeding her treats and watching the world go by to begin with, that would be a good start. You need to be doing lots and lots of trips like that in as many different places as you can manage. People will most probably stop and speak to you, as they always do with pups and if you just explain that she's a rescue and needs space while she gets used to people, but they can help by tossing her a treat or two, most people are only too willing to help out.
Socialisation classes will help a lot too. Don't be surprised if she spends the first couple of lessons hiding and if she does - and it's a decent class - she should be allowed to do so. Even if it means you have to attend two courses consecutively as it takes the whole of the first course for her to find her confidence then it's still better to take it at her pace. My old girls spent the first few puppy classes hiding under a stack of chairs refusing to come out, then one week she just decided she was finally brave enough and made a friend or two. She was never highly sociable - as in seeking out affection from people outside of the family - and definitely preferred her own family to outsiders, but she was friendly enough and would say a nice hello and allow herself to be petted before going off and doing her own thing.
Stick with it, you'll get there. You have done an amazing thing by taking on rescue and she's a very lucky girl to have you.