Can't see any options other than you outlined. Income isn't high enough to get more than 160ish mortgage.
Option 1. You'd be making an offer to buy, subject to sale of your own house. If there's already interest the seller wouldn't entertain this. Plus ideally you need a cash buyer so you can close sale quickly. Talk to the agent, and see what kind of interest there might be in your home. Agent might help convince sellers to wait if they are getting commission from sale of your home as well.
Option 2. You should be able to get a mortgage for 160. Banks treat bonuses differently - I'd go to a broker to work through the best option. You've also got the potential rental income on a debt free property.
You'll need parents to sign a letter that the funds are a gift - needs to be made to their child, and not the couple, to avoid tax leakage.
If you rent house, since there's no mortgage you've no interest expense for tax. But you've some headroom to earn rent at lower tax rate.
Option 3. Really as above.