"I go slowly on a narrow road."
I am Japanese and I can understand that we tend to put は in this case, but the subject in this sentence is 私, which we do not have to put. を is better in this case, I think. 細い道をゆっくりすすみます should be the answer.
I completely agree with you. I asked 2 Japanese friends of mine as well and they both said the same thing. I think they made an error here.
This answer seems to indicate the narrow road is the subject. Would を or に make more sense than は?
That is because the key point in this sentence is 'a narrow road' rather than 'I go'. Since the road is narrow, it is harder to go on.
When we put は in this case, there must be some sentences before this sentence: such as 太い道は速く、細い道はゆっくりと進みます。(We go fast on a wide road, but we go slowly on a narrow road.) は can be used when you want to compare 2 things, and we sometimes use は for the latter. For example, 私は彼女にプレゼントをあげるけど、彼はいいだろう。(I give her a present, but not to him.)
The use of は here implies that the speaker is comparing narrow roads to something else. For example, as "I go slowly on narrow roads, but not on wide roads"
I'm no expert, but I think this is a bit misleading for beginners without more context or explanation about why は is being used.
進み (すすみ) translates as "progress". Which makes sense to me in this sentense as it has no fixed (implicited) destination.
In a sentese with implied destination i would use ikimase, ikimase, or kaerimasu.