L1B eligibility for part-time employee and other paths to relocate to USA

[adamas]

I am working in the UK for a branch of a US-based company. I am formally employed by the UK branch, but I am working part-time for them. Actually the contract states that I have to work at least 60 hours per month, but does not state specifically a fixed number of hours nor a maximum amount of hours per month.
My employment started in January 2016 and the company's and my plan would be to relocate to the US ideally in the summer 2017.

Under this circumstances, will I be eligible for a L1B visa, after one year of employment (i.e. January 2017), or given that I am not working full-time I will not?

What would be then the best path to relocate to the US? I am a specialized worker with an advanced degree (equivalent of MSc) and next spring I should also be awarded a PhD, which I am finishing right now.

I know that one option is the H1B visa, but, as far as I am aware, there are much more applications than places available. What happens in this case?

Would instead be possible to bypass the visa step and apply directly for the green card from abroad? How likely will this be successful?
I am an Italian citizen, so I guess that the waiting time is less than other nationalities.

Thank you.