I've always wanted to do game writing but I've always had the same sort of block. I was never sure how to get into it, and I never had or perhaps made the time to do the necessary leg work. I've written some games, but it's always been a case of 'with' and not 'for' and because it was working with the IP of others it was never going to be a paying opportunity.
8000 words a day is mental. Stephen King, a most prolific man himself, aims for 2-3000 words a day. With a 5 day work week @2000/day that's still half a million words a year.
I haven't hired writers myself for many years (largely because the profit margins for a small company like mine can't justify the expense). I write everything myself now so take my advice with a grain of salt. But when I got into this, what I did was send query letters to companies I liked. It is a question of what they are looking for and if you have the writing ability, the passion, and ( perhaps unfortunately today, the social media reach) to make it worth them paying you. What I found was writing a query letter often led to a request for a proposal. I would say try to be thick skinned if you can. Also one thing I've observed is few companies are looking for a new game (I am sure that happens, but mostly what I've encountered is people wanting supplements and support for existing lines, or someone to work on a game they are developing). You wouldn't want to write a whole game then shop it around, you would want to send a query about the game, and see if there is interest first. But you will likely have much better luck writing queries that fit the current line of projects the company seems to have (still it is a small industry, it is quirky enough that an odd or cool idea might land with a publisher and you likely can reach them by email or through social media).