What isn't working
Pushing Jane towards reading isn’t working. It is likely that it sets up an oppositional dynamic with the adults around her.
To date she has defensively insisted that she doesn’t care what people think or how the board game goes. She can’t back down from that stance without feeling vulnerable, if she drops her defence the adults ‘win’ and she loses.
It may be that this isn’t the moment for either overt rewards or for appeals to logic, or indeed anything that draws attention to whether she is reading or not. It might well be the time to be sneaky and give her space to back down from that stance without remark.
Consider how you might use subtly set up circumstances where she can drift towards reading of her own volition, such that she doesn’t think anyone else is involved. It is interpersonal skills, but the trick may be to make the involvement of the adults concerned as invisible to her as possible.
First have a think about whether anything is undermining the message that reading is a good and normal thing
Does she see adults around her reading for pleasure? Does she hear
them talking to each other about what they read?
Are there reading materials lying about the place?
Are there often other diversions and attention catchers available to
her? Is the TV or radio often on, can she watch DVDs on demand, play
games on a tablet etc?
In much the way that relieving insomnia requires good ‘sleep-hygiene’, getting over not-reading may require good ‘entertainment hygiene’.
Where Sleep hygiene requires limiting exposure to activities which compete with your ability to sleep, entertainment hygiene would require limiting exposure to and accessibility of competing audio/visual inputs or activities.
Environment
Aim to create a situation where, whether it is for an hour or so every evening or a couple of evenings a week; other entertainments are not activated. I don’t mean make a big production about turning off the television and announcing ‘now we shall have reading time’, just don’t turn it on.
If necessary start with a very short period and don’t be afraid to stage manage it at first if that helps to break old habits.
At a time when the TV, radio or computer would usually be switched on, something like this could happen:
Adult 1: who might already be reading some fiction
can we just leave it off for a few minutes while I finish reading
this?
Adult 2: picking up their own book
No worries
After 10-15 minutes or whatever seems good:
Adult 1: putting aside book.
Thanks for that, I was just at the bit where the dinosaurs had the
aliens cornered
(or whatever floats your boat but might plausibly pique Jane’s curiosity too.)
Adult 2: looking up enthusiastically
Oh, I loved that bit, wait until you get to… Oh, no I’d better not
say… spoilers!
And then the TV goes on and things carry on as usual.
But don’t immediately suggest that Jane read too. Just make sure there are things around that she could read if she felt like it but maybe stuff that the adults also read.
'Age appropriate' materials
In my first answer I focused on the type of reading material which had captured my reading imagination, but that wasn’t about interpersonal skills and I’ve deleted it. But one of the things I spoke about was some of the reading material I enjoyed at the time I was getting over my own ‘Jane-like’ reading resistance.
Having eventually had my reading imagination captured by cartoon strips about a girl called Beryl the Peril who was anti-establishment, not 'childish', who made things happen if she was bored and who often got the better of her parents (she didn't much mind any punishments). I spend half my pocket money on Peanuts books, moving onto BC and more recently all of Calvin and Hobbes.
What those have in common is that they are accessible without being 'childish' or even 'for' children and though individual strips often stand alone, there is a world and often a wider story arc linking them. In Charlie brown, Linus, Calvin and Snoopy, there is a lot for a self-sufficient, imaginative or or not-one-of-the-crowd child to identify with.
So, as an adjunct to the IP skills of leading by example and creating a conducive environment and de-emphasising the necessity of reading, my suggestion would be to look for some kind of longer form comic strip. I'm not sure what's available in comic books in your country, whether there are things that aren't all super heroes, but look for something that isn't just the four-frame funnies. Look out for a full page 15-20 frame strips with room for some story development in each tale, a wider story/world arc and perhaps published weekly or fortnightly so that it comes as a drip feed, building anticipation. But here's the thing, don't tell Jane you got them for her to practice reading on, just have the adults read them themselves, quibble over whose turn it is, laugh while reading them, be seen to enjoy them!
I'm not familiar with graphic novels, but there might be good characters to be found in that section of the bookshop.
TL:DR
Don’t try to push Jane into the pool while you are all at the edge, let her see you all splashing about and leave some water wings handy.