Hi,
NO! Don't use a slide hammer or force of any kind or you will regret it. It will probably never shift again if you try that.
Honda calls that piece the "water pump housing" for some reason but it's really the base of the housing.
Sadly, in order to remove it, it is necessary to remove the propshaft holder with transmission and then remove the bevel gear and then slide the mainshaft out.
The main reason for this misery is that the shift shaft is being held by a pin to the underside of that piece or "housing".
The little "shoe" (Honda calls it a "pushrod") that selects the gears is pinned to the bottom of that shift shaft and is catching down there. That's the metal "thunk" you are hearing.
Once the transmission is removed you might be able to manipulate the shift shaft and shoe enough to slide the thing up but I believe you'll find that it won't slide up off of the mainshaft because the shaft splines are too large.
I've only done it a few times and I don't have fond memories of the job. But....it's certainly do-able.
Sorry to be the one to give you the bad news.
Good luck.