Hold a feather toy just above your lens to get them to look right at you.
ErrantWhimsy
Can you both be holding something, like could your partner be handing you a flower bouquet? For the book idea, what about sitting close to each other on a park bench reading the same book, or one of you holding a book and the other turning the page for them? Sitting at a picnic blanket and handing each other a sandwich?
That's because you seem to think pictures sell photography, and that's just not true. The photographer sells their photography. You have to learn marketing and sales in order to run a business. What does "trying very hard to get work" look like? What are you actually doing to get bookings?
Do you know who your target client is? What are you doing to reach them specifically? Are you selling digitals, mini sessions, prints? Are you a luxury service or a shoot and burn service? How do you make clients feel during sessions? How do you promote loyalty with current clients? What are you doing to increase the odds of word of mouth referrals?
Here's my challenge to you: go make a list of those people with little talent but lots of bookings and really observe their website and social media presence. Take notes on what they're doing to make their clients feel special, taken care of, and what makes the photographer stand out. Pay attention to how they price the photo session vs. digital files vs. prints. If you can, book sessions with a few of them and see how they interact with you and how they price their services. Or message them and see if they'd be up for a 30 minute zoom call to teach you about how they manage their business (pick people in a different physical location so you aren't competitors).
Ask your office to purchase a backdrop and a lighting setup for you at the very least. You can get a basic cheap continuous lighting softbox and a backdrop for about $200.
I have a friend who is a famous fine art photographer with millions of followers. Like 95% of her photos are of herself! She'll just go out in the woods or in her garage studio and take the picture she wants then she does amazing photoshop work.
You'll want a long lens, ideally something that goes to at least 200mm. I use a 70-300mm lens for wildlife.
I would say look at Sony mirrorless like an A6000 and see if you can get an older used camera and lens for that budget. They had superior autofocus in the camera body years you'll be able to get with that.