Welcome to the board!
You've given a bit of a tall order, inasmuch you're right that you won't find a large harp in your price bracket. Normally I would suggest you look for a good used machine (it's still unlikely you'd one with a large harp), but that's no good if you want to use your Amazon voucher.
Unfortunately machines at your price point are often made of lightweight plastic and tend to be lighter, ergo not 'sturdy' enough for what you want it to do. I am speaking about here in the UK however, and there's more choice in the US (as well as cheaper), so someone else may come up with a suggestion.
Another suggestion might be to save for a little longer for a machine with better features, if that's an option for you.
I'm not exactly sure what you mean by 'steering' - could you explain a little more please? Happy Quilting!