Strategies for low spots in fields

Many, no all of you have this problem as do I:
You have good fields, but many have low spots, some hold water and never quite dry.
A few of you, like myself, cannot fill the low spots, they must remain low for one reason or another.
So what's your haying strategy? When your fields are ready to cut, they may have standing water or mud in the low spots. I have some areas that are 1/4-1/2 acre, so I can't leave them un hayed.

What I have done is cut all the hay, then bale all the dry areas as normal but go around the low areas. Then I rake the hay out of the mud area onto dry area and come back to get it in a day. Big loss of efficiency. Even with applicator, it's too damp to bale safely.

I tried raking the hay out of damp area immediately after cutting into the dry areas, but then it's too thick and won't dry.

I don't think there is an alternate strategy, but can anyone enlighten this self taught greenhorn with some other ideas?
Should I cut around them and bush hog later? This is also inefficient and wastes time.

Strategies for low spots in fields