But first, let's consider a couple of questions before we get to the heart of your question. WHO is your intended audience for this film? Are you thinking your script might be an 'art house' piece? Maybe you're planning something experimental. NO, you're hoping for that mega-blockbuster at the local movie theater? You need to rethink your prejudice against 3 act structure. The closer you get to mainstream in intent - the more thoroughly your script should be grounded in 3 acts; beginning, middle and end (or resolution).
Next, let's look at your bias against the 3 act structure. It IS true that some really terrible movies have been created within the context of this format. But WOW, what about all the really inventive films that have also adhered to it? Films like Shakespeare in Love, Being John Malkovich, Juno, The Fall and American Beauty were all firmly grounded in the 3 act structure. What gives?
Many beginning screenwriters lay some really BAD MOVIES at the feet of the 3 act structure. But writing screenplays is a lot like writing sonnets (you know Shakespeare- iambic pentameter) in that it's a strict format that can produce some absolutely timeless writing. For instance, Shakespeare's 'Shall I compare Thee to a Summer Day?'. Or... the really horrible sonnet I wrote in my sophomore English Lit class.
Great sonnets, like great screenplays, challenge the writer to search for a completely fresh aspect on a timeless theme and then tests their inventiveness in pouring their story idea into a jug of very specific proportions. The bad movies you've seen aren't a result of the 3 act structure; but a result of the lack of skill or persistence on the part of the writer!
I hope this helps. And I do wish you luck with your screenplay - and let me know when you've finished it. I'd love to read your work.