The block plane was originally made for flattening butchers blocks, hence the name or so legend has it . If the use is endgrain then the mouth size is irrelevant as there are no chips to break, it's all short grain shavings. The really cool thing about these planes is that the bevel on the iron is uppermost so the cutting geometry is variable a shallow angle (25 degreed iron vevel and iron angle combined)) for endgrain or a steeper one(40-45) for long grain or a very steep one (50-55) for very difficult woods like east Indian Satinwood. You don't need a regrind for the angle change just hone at the different angle, that's all you need but a regrind will more than likely be needed if you need to hone at a shallower angle than the last hone if that makes sense.
If you're hollowing you need to change your planing technique. At the start of the cut press down on the front of the plane and transfer the pressure as the plane moves forward. You don't actually push the plane as such but lock your arms to your sides and rock forwards keeping your eye over the mouth of the plane. It should be done quite slowly so you keep absolute control over the shaving, it should come off full width for the whole length of the wood once it's flat. An hour practising should see you set for life. Precise work needs a different mindset to hanging a kitchen door, speed comes from getting it right first time not doing it quickly, gossamer thin shavings you can see through are what you should be seeing. Once you can do that (and it's not hard) you can do anything