I forgot the verb for proceeding with/despite difficulty, when talking about a process. It's '[something] ahead' (but you may feel free to offer something without 'ahead'). Like 'forge ahead' but with a different meaning. Like
Since the autocrat's ouster, the reforms in the country are [verb]ing ahead [along?], and the reaction sentiment is getting stronger.
or, a bit different
We hit a few snags, but the project is [verb]ing ahead.
In both examples, it's proceeding with difficulty. The difference is the first sentence stresses difficulty (the reforms are slow, people get disillusioned), the second proceeding (it's coming to fruition nonetheless, everything's fine).
Best Answer
Maybe the word you are looking for is slog.
For example,