1)
Invalid contract (if not signed by owner)
Even if the OP gets it stamped now (late applications are allowed, you just pay more than the usual fee), the contract is still not signed by actual owner or the owner’s Power of Attorney (according to what the Landlord now claims).
And having no valid signature probably cancels out having a break clause on the contract.
2)
Dodgy greedy landlord
Always a good reason not to renew a contract.
Find a new place to move to and as others advised, check the owner of your next potential rental property on the online land search (if you do not use an agent, you can check it yourself easily online, I think it’s only about $10), read the contract carefully and look out for things like a break clause (2 years, 1 year fixed, 1 year option is most common, or you can try negotiate a longer fixed period if you want to stay longer). Though you don’t like moving, with a better rental situation, you can be much happier.The landlord could probably want you to move out before you’ve stayed the 2 years for his own reason (wants to use for himself or for a friend or family member?) anyway, so he probably doesn’t expect you to agree to the 20% rent hike (unless you’re paying very low rent) but to move out instead.
The only other caution I can think of is if you do move out before the 24 months, and you are actually obliged to pay the full 24 months rent (the landlord lied before and suddenly can provide a Power of Attorney for his relative who signed the contract so the contract is actually valid?).
As others suggest, get legal advice from a lawyer first. And if possible, communicate with the Landlord in writing (text, WhatsApp, email), not phone calls, so you can use it as evidence.