Placed on another project without any consultation or providing prior understanding of role/project. I understand I'm a second year, but this attitude seriously turns me off from consulting.

You need to network, it's a big Firm and it's very important whom do you know....

Would finding your own next project before landing on the beach prevent that from happening?

It's very common at the firm. HR does not care anything about you.

I feel like this is a uniquely PwC problem

Happens at Deloitte all the time in your first year or two. The key is to network and build relationships with managers who are on projects you want to be on, get them to staff you, then kill it on those projects. If you do well they'll keep staffing you, and HR can't put you on other stuff if you are already staffed. As long as you have open time on your schedule, HR will grab you when they need to staff a project, because all that matters to them is that they get a warm body there, no one cares if you want to be there or know what the hell you're doing

I have been doing all the above but nothing ever seems to work out in terms of timing. Sigh.

Not really a problem at ACN except for your first project or if you have literally no network. Technically you always have the right to say no here, it's just not always necessarily the smartest move.