Splitting a 5610 without dual tanks is a piece of cake. With air tools, I could have it apart in less than 30 minutes. It would be far preferable compared to dinking around through the 3-point top cover opening.
As Rod said, you MAY be able to fish it out through the top, but there's also a good chance you can't - I've never tried it. There's a very good chance you could waste several hours in that potentially fruitless adventure.
Also, you're supposed to adjust the new brake band with the band on the housing, which is something you cannot do if you go through the top.
The biggest pain with a rear split is joining the two cases back together. Do yourself a big favor and chamfer the splines in the PTO hub with a small grinder. This goes a long way towards making that job go much smoother.