I live in an amenity building owned by a large developer.

I have renewed my lease twice since moving to my current apartment and have had success lowering the proposed increase. Leverage points are: availability levels in your building, asking rents for availabilities in the building (monitor this closely and take screenshots as rates fluctuate), rates for similar age/quality buildings nearby and threaten to move (again, take screenshots). You are an established tenant so the landlord should want to keep you and not have to turn over your unit (by monitoring availability in your building you can tell if leasing is slow). Open the conversation with them saying you have enjoyed living in the building and want to renew, you were expecting an increase but not as high as the proposal (maybe propose a counteroffer but lowball it to just pad where you're okay ending up), and are hoping you can come to a reasonable agreement. Good luck!

U-Haul's website has a feature where you can search for "labor only" movers. I've had good experience with Honeymovers in the past.