She sounds very confused & perhaps has had some 'bad' desensitising training in the past, or likely your last comment about being an orphan without any experience of learning from other horses is what it boils down to. Time & again I've heard these sorts of stories about horses socially starved of other horses, but I've never had personal experience of an orphan that's truly never had other horses - many who have spent their whole adulthood in solitary confinement from their species though.
As this sounds like an extra difficult horse & you sound confused too, I'd suggest finding someone with experience to help you. At any rate, another helper would allow you to do things differently. I also suggest learning the principles of 'clicker training' as an invaluable 'tool' for any kind of training, and learn where/how to use positive reinforcement effectively.
As you say she's learned well how to yield to halter pressure, I'd make the most of that. If you have a helper, have them at her head holding the lead. If not, you'll have to be in a sort of leading position to do both. Start out applying light pressure behind her, rythmic & continual, and if/when she doesn't get it, 'back it up' with very light halter pressure. The instant she *starts* to think about forward, drop all pressure. With repetition, you should soon be able to do this without halter pressure or her reactivity.
When you then go to ask her without someone at her head, she should have had enough practice to understand. But if not, you need to elicit the behaviour in the first place, before you can strengthen and shape it, so I think getting her to move forward in any form - even if bolting to begin with - is a reasonable first step. I'd escalate that pressure behind her gradually, so she'll get the idea that she can avoid harder pressure by responding to the early signals. Then with repetition she will learn that the pressure in that place just means move forward.
The second part - her wanting to 'jump in your lap' when she feels threatened is also obviously a problem to be resolved. I would teach this first, that she must stay out of your personal 'bubble' *at all times*(consistently - I wouldn't even invite her in until much later in the training, considering). I'd consider starting out teaching this with a barrier(fence, gate, etc) between you & I'd teach her things like moving forward, where she feels threatened & confused, with a barrier between, so you can stay safe & do what's necessary.
I generally don't agree with getting really 'heavy' with a horse or doing things that frighten them. In the situation above, when she's trying to climb on you, it may well be in confusion & fear, her reacting without thinking. Regardless, remember it's nothing against you, just the way she's been brought up, so don't blame her or think of her as deserving punishment or such. BUT In that sort of situation, it comes down to safety(you won't always have a fence between you), so I would probably get VERY BIG to break through her unthinking reaction, to cause her to be more frightened of jumping on you. That is one of the few situations when I think causing her to think the sky is falling is probably warranted.
Now, hopefully someone with experience of orphans comes along to give you other suggestions!